Tabelul integralelor nedeterminate ale funcțiilor iraționale

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Această pagină conține un tabel de integrale nedeterminate ale funcțiilor iraționale . Pentru alte integrale, consultați Tabelele de integrale .

\int {\sqrt {a^{2}-x^{2}}}\;\mathrm {d} x={\frac {1}{2}}\left(x{\sqrt {a^{2}-x^{2}}}+a^{2}\arcsin {\frac {x}{a}}\right)\qquad {\mbox{(}}|x|\leq |a|{\mbox{)}}

{\ displaystyle \ int {\ sqrt {a ^ {2} -x ^ {2}}} \; \ mathrm {d} x = {\ frac {1} {2}} \ left (x {\ sqrt {a ^ {2} -x ^ {2}}} + a ^ {2} \ arcsin {\ frac {x} {a}} \ right) \ qquad {\ mbox {(}} | x | \ leq | a | {\ mbox {)}}}

{\ displaystyle \ int {\ sqrt {a ^ {2} -x ^ {2}}} \; \ mathrm {d} x = {\ frac {1} {2}} \ left (x {\ sqrt {a ^ {2} -x ^ {2}}} + a ^ {2} \ arcsin {\ frac {x} {a}} \ right) \ qquad {\ mbox {(}} | x | \ leq | a | {\ mbox {)}}}

\int x{\sqrt {a^{2}-x^{2}}}\;\mathrm {d} x=-{\frac {1}{3}}{\sqrt {(a^{2}-x^{2})^{3}}}\qquad {\mbox{(}}|x|\leq |a|{\mbox{)}}

{\ displaystyle \ int x {\ sqrt {a ^ {2} -x ^ {2}}} \; \ mathrm {d} x = - {\ frac {1} {3}} {\ sqrt {(a ^ {2} -x ^ {2}) ^ {3}}} \ qquad {\ mbox {(}} | x | \ leq | a | {\ mbox {)}}}

{\ displaystyle \ int x {\ sqrt {a ^ {2} -x ^ {2}}} \; \ mathrm {d} x = - {\ frac {1} {3}} {\ sqrt {(a ^ {2} -x ^ {2}) ^ {3}}} \ qquad {\ mbox {(}} | x | \ leq | a | {\ mbox {)}}}

\int {\frac {{\sqrt {a^{2}-x^{2}}}\;\mathrm {d} x}{x}}={\sqrt {a^{2}-x^{2}}}-a\log \left|{\frac {a+{\sqrt {a^{2}+x^{2}}}}{x}}\right|\qquad {\mbox{(}}|x|\leq |a|{\mbox{)}}

{\ displaystyle \ int {\ frac {{\ sqrt {a ^ {2} -x ^ {2}}} \; \ mathrm {d} x} {x}} = {\ sqrt {a ^ {2} - x ^ {2}}} - a \ log \ left | {\ frac {a + {\ sqrt {a ^ {2} + x ^ {2}}}} {x}} \ right | \ qquad {\ mbox {(}} | x | \ leq | a | {\ mbox {)}}}

{\ displaystyle \ int {\ frac {{\ sqrt {a ^ {2} -x ^ {2}}} \; \ mathrm {d} x} {x}} = {\ sqrt {a ^ {2} - x ^ {2}}} - a \ log \ left | {\ frac {a + {\ sqrt {a ^ {2} + x ^ {2}}}} {x}} \ right | \ qquad {\ mbox {(}} | x | \ leq | a | {\ mbox {)}}}

\int {\frac {\mathrm {d} x}{\sqrt {a^{2}-x^{2}}}}=\arcsin {\frac {x}{a}}\qquad {\mbox{(}}|x|\leq |a|{\mbox{)}}

{\ displaystyle \ int {\ frac {\ mathrm {d} x} {\ sqrt {a ^ {2} -x ^ {2}}}} = \ arcsin {\ frac {x} {a}} \ qquad { \ mbox {(}} | x | \ leq | a | {\ mbox {)}}}

{\ displaystyle \ int {\ frac {\ mathrm {d} x} {\ sqrt {a ^ {2} -x ^ {2}}}} = \ arcsin {\ frac {x} {a}} \ qquad { \ mbox {(}} | x | \ leq | a | {\ mbox {)}}}

\int {\frac {x^{2}\;\mathrm {d} x}{\sqrt {a^{2}-x^{2}}}}=-{\frac {x}{2}}{\sqrt {a^{2}-x^{2}}}+{\frac {a^{2}}{2}}\arcsin {\frac {x}{a}}\qquad {\mbox{(}}|x|\leq |a|{\mbox{)}}

{\ displaystyle \ int {\ frac {x ^ {2} \; \ mathrm {d} x} {\ sqrt {a ^ {2} -x ^ {2}}}} = - {\ frac {x} { 2}} {\ sqrt {a ^ {2} -x ^ {2}}} + {\ frac {a ^ {2}} {2}} \ arcsin {\ frac {x} {a}} \ qquad { \ mbox {(}} | x | \ leq | a | {\ mbox {)}}}

{\ displaystyle \ int {\ frac {x ^ {2} \; \ mathrm {d} x} {\ sqrt {a ^ {2} -x ^ {2}}}} = - {\ frac {x} { 2}} {\ sqrt {a ^ {2} -x ^ {2}}} + {\ frac {a ^ {2}} {2}} \ arcsin {\ frac {x} {a}} \ qquad { \ mbox {(}} | x | \ leq | a | {\ mbox {)}}}

\int {\sqrt {x^{2}+a^{2}}}\;\mathrm {d} x={\frac {1}{2}}\left(x{\sqrt {x^{2}+a^{2}}}+a^{2}\,\log \left(x+{\sqrt {x^{2}+a^{2}}}\right)\right)={\frac {1}{2}}\left(x{\sqrt {x^{2}+a^{2}}}+a^{2}\,\mathrm {arsinh} {\frac {x}{a}}\right)

{\ displaystyle \ int {\ sqrt {x ^ {2} + a ^ {2}}} \; \ mathrm {d} x = {\ frac {1} {2}} \ left (x {\ sqrt {x ^ {2} + a ^ {2}}} + a ^ {2} \, \ log \ left (x + {\ sqrt {x ^ {2} + a ^ {2}}} \ right) \ right) = {\ frac {1} {2}} \ left (x {\ sqrt {x ^ {2} + a ^ {2}}} + a ^ {2} \, \ mathrm {arsinh} {\ frac {x } {a}} \ right)}

{\ displaystyle \ int {\ sqrt {x ^ {2} + a ^ {2}}} \; \ mathrm {d} x = {\ frac {1} {2}} \ left (x {\ sqrt {x ^ {2} + a ^ {2}}} + a ^ {2} \, \ log \ left (x + {\ sqrt {x ^ {2} + a ^ {2}}} \ right) \ right) = {\ frac {1} {2}} \ left (x {\ sqrt {x ^ {2} + a ^ {2}}} + a ^ {2} \, \ mathrm {arsinh} {\ frac {x } {a}} \ right)}

\int x{\sqrt {x^{2}+a^{2}}}\;\mathrm {d} x={\frac {1}{3}}{\sqrt {(x^{2}+a^{2})^{3}}}

{\ displaystyle \ int x {\ sqrt {x ^ {2} + a ^ {2}}} \; \ mathrm {d} x = {\ frac {1} {3}} {\ sqrt {(x ^ { 2} + a ^ {2}) ^ {3}}}}

{\ displaystyle \ int x {\ sqrt {x ^ {2} + a ^ {2}}} \; \ mathrm {d} x = {\ frac {1} {3}} {\ sqrt {(x ^ { 2} + a ^ {2}) ^ {3}}}}

\int {\frac {{\sqrt {x^{2}+a^{2}}}\;\mathrm {d} x}{x}}={\sqrt {x^{2}+a^{2}}}-a\log \left|{\frac {a+{\sqrt {x^{2}+a^{2}}}}{x}}\right|

{\ displaystyle \ int {\ frac {{\ sqrt {x ^ {2} + a ^ {2}}} \; \ mathrm {d} x} {x}} = {\ sqrt {x ^ {2} + a ^ {2}}} - a \ log \ left | {\ frac {a + {\ sqrt {x ^ {2} + a ^ {2}}}} {x}} \ right |}

{\ displaystyle \ int {\ frac {{\ sqrt {x ^ {2} + a ^ {2}}} \; \ mathrm {d} x} {x}} = {\ sqrt {x ^ {2} + a ^ {2}}} - a \ log \ left | {\ frac {a + {\ sqrt {x ^ {2} + a ^ {2}}}} {x}} \ right |}

\int {\frac {\mathrm {d} x}{\sqrt {x^{2}+a^{2}}}}=\mathrm {arsinh} {\frac {x}{a}}=\log \left|x+{\sqrt {x^{2}+a^{2}}}\right|

{\ displaystyle \ int {\ frac {\ mathrm {d} x} {\ sqrt {x ^ {2} + a ^ {2}}}} = \ mathrm {arsinh} {\ frac {x} {a}} = \ log \ left | x + {\ sqrt {x ^ {2} + a ^ {2}}} \ right |}

{\ displaystyle \ int {\ frac {\ mathrm {d} x} {\ sqrt {x ^ {2} + a ^ {2}}}} = \ mathrm {arsinh} {\ frac {x} {a}} = \ log \ left | x + {\ sqrt {x ^ {2} + a ^ {2}}} \ right |}

\int {\frac {x\,\mathrm {d} x}{\sqrt {x^{2}+a^{2}}}}={\sqrt {x^{2}+a^{2}}}

{\ displaystyle \ int {\ frac {x \, \ mathrm {d} x} {\ sqrt {x ^ {2} + a ^ {2}}}} = {\ sqrt {x ^ {2} + a ^ {2}}}}

{\ displaystyle \ int {\ frac {x \, \ mathrm {d} x} {\ sqrt {x ^ {2} + a ^ {2}}}} = {\ sqrt {x ^ {2} + a ^ {2}}}}

\int {\frac {x^{2}\;\mathrm {d} x}{\sqrt {x^{2}+a^{2}}}}={\frac {x}{2}}{\sqrt {x^{2}+a^{2}}}-{\frac {a^{2}}{2}}\,\mathrm {arsinh} {\frac {x}{a}}={\frac {x}{2}}{\sqrt {x^{2}+a^{2}}}-{\frac {a^{2}}{2}}\log \left|x+{\sqrt {x^{2}+a^{2}}}\right|

{\ displaystyle \ int {\ frac {x ^ {2} \; \ mathrm {d} x} {\ sqrt {x ^ {2} + a ^ {2}}}} = {\ frac {x} {2 }} {\ sqrt {x ^ {2} + a ^ {2}}} - {\ frac {a ^ {2}} {2}} \, \ mathrm {arsinh} {\ frac {x} {a} } = {\ frac {x} {2}} {\ sqrt {x ^ {2} + a ^ {2}}} - {\ frac {a ^ {2}} {2}} \ log \ left | x + {\ sqrt {x ^ {2} + a ^ {2}}} \ right |}

{\ displaystyle \ int {\ frac {x ^ {2} \; \ mathrm {d} x} {\ sqrt {x ^ {2} + a ^ {2}}}} = {\ frac {x} {2 }} {\ sqrt {x ^ {2} + a ^ {2}}} - {\ frac {a ^ {2}} {2}} \, \ mathrm {arsinh} {\ frac {x} {a} } = {\ frac {x} {2}} {\ sqrt {x ^ {2} + a ^ {2}}} - {\ frac {a ^ {2}} {2}} \ log \ left | x + {\ sqrt {x ^ {2} + a ^ {2}}} \ right |}

\int {\frac {\mathrm {d} x}{x{\sqrt {x^{2}+a^{2}}}}}=-{\frac {1}{a}}\,\mathrm {arsinh} {\frac {a}{x}}=-{\frac {1}{a}}\log \left|{\frac {a+{\sqrt {x^{2}+a^{2}}}}{x}}\right|

{\ displaystyle \ int {\ frac {\ mathrm {d} x} {x {\ sqrt {x ^ {2} + a ^ {2}}}}} = - {\ frac {1} {a}} \ , \ mathrm {arsinh} {\ frac {a} {x}} = - {\ frac {1} {a}} \ log \ left | {\ frac {a + {\ sqrt {x ^ {2} + a ^ {2}}}} {x}} \ right |}

{\ displaystyle \ int {\ frac {\ mathrm {d} x} {x {\ sqrt {x ^ {2} + a ^ {2}}}}} = - {\ frac {1} {a}} \ , \ mathrm {arsinh} {\ frac {a} {x}} = - {\ frac {1} {a}} \ log \ left | {\ frac {a + {\ sqrt {x ^ {2} + a ^ {2}}}} {x}} \ right |}

\int {\sqrt {x^{2}-a^{2}}}\;\mathrm {d} x={\frac {1}{2}}\left(x{\sqrt {x^{2}-a^{2}}}\mp a^{2}\,\mathrm {arcosh} \left|{\frac {x}{a}}\right|\right)\qquad {\mbox{(per }}|x|\geq |a|{\mbox{; }}-{\mbox{ per }}x>0{\mbox{, }}+{\mbox{ per }}x<0{\mbox{)}}

{\ displaystyle \ int {\ sqrt {x ^ {2} -a ^ {2}}} \; \ mathrm {d} x = {\ frac {1} {2}} \ left (x {\ sqrt {x ^ {2} -a ^ {2}}} \ mp a ^ {2} \, \ mathrm {arcosh} \ left | {\ frac {x} {a}} \ right | \ right) \ qquad {\ mbox {(pentru}} | x | \ geq | a | {\ mbox {;}} - {\ mbox {pentru}} x> 0 {\ mbox {,}} + {\ mbox {pentru}} x <0 { \ mbox {)}}}

{\ displaystyle \ int {\ sqrt {x ^ {2} -a ^ {2}}} \; \ mathrm {d} x = {\ frac {1} {2}} \ left (x {\ sqrt {x ^ {2} -a ^ {2}}} \ mp a ^ {2} \, \ mathrm {arcosh} \ left | {\ frac {x} {a}} \ right | \ right) \ qquad {\ mbox {(pentru}} | x | \ geq | a | {\ mbox {;}} - {\ mbox {pentru}} x> 0 {\ mbox {,}} + {\ mbox {pentru}} x <0 { \ mbox {)}}}

\int x{\sqrt {x^{2}-a^{2}}}\;\mathrm {d} x={\frac {1}{3}}{\sqrt {(x^{2}-a^{2})^{3}}}\qquad {\mbox{(per }}|x|\geq |a|{\mbox{)}}

{\ displaystyle \ int x {\ sqrt {x ^ {2} -a ^ {2}}} \; \ mathrm {d} x = {\ frac {1} {3}} {\ sqrt {(x ^ { 2} -a ^ {2}) ^ {3}}} \ qquad {\ mbox {(for}} | x | \ geq | a | {\ mbox {)}}}

{\ displaystyle \ int x {\ sqrt {x ^ {2} -a ^ {2}}} \; \ mathrm {d} x = {\ frac {1} {3}} {\ sqrt {(x ^ { 2} -a ^ {2}) ^ {3}}} \ qquad {\ mbox {(for}} | x | \ geq | a | {\ mbox {)}}}

\int {\frac {{\sqrt {x^{2}-a^{2}}}\;\mathrm {d} x}{x}}={\sqrt {x^{2}-a^{2}}}-a\arcsin {\frac {a}{x}}\qquad {\mbox{(per }}|x|\geq |a|{\mbox{)}}

{\ displaystyle \ int {\ frac {{\ sqrt {x ^ {2} -a ^ {2}}} \; \ mathrm {d} x} {x}} = {\ sqrt {x ^ {2} - a ^ {2}}} - a \ arcsin {\ frac {a} {x}} \ qquad {\ mbox {(for}} | x | \ geq | a | {\ mbox {)}}}

{\ displaystyle \ int {\ frac {{\ sqrt {x ^ {2} -a ^ {2}}} \; \ mathrm {d} x} {x}} = {\ sqrt {x ^ {2} - a ^ {2}}} - a \ arcsin {\ frac {a} {x}} \ qquad {\ mbox {(for}} | x | \ geq | a | {\ mbox {)}}}

\int {\frac {\mathrm {d} x}{\sqrt {x^{2}-a^{2}}}}=\mathrm {arcosh} {\frac {x}{a}}=\log \left(|x|+{\sqrt {x^{2}-a^{2}}}\right)\qquad {\mbox{(per }}|x|>|a|{\mbox{)}}

{\ displaystyle \ int {\ frac {\ mathrm {d} x} {\ sqrt {x ^ {2} -a ^ {2}}}} = \ mathrm {arcosh} {\ frac {x} {a}} = \ log \ left (| x | + {\ sqrt {x ^ {2} -a ^ {2}}} \ right) \ qquad {\ mbox {(for}} | x |> | a | {\ mbox {)}}}

{\ displaystyle \ int {\ frac {\ mathrm {d} x} {\ sqrt {x ^ {2} -a ^ {2}}}} = \ mathrm {arcosh} {\ frac {x} {a}} = \ log \ left (| x | + {\ sqrt {x ^ {2} -a ^ {2}}} \ right) \ qquad {\ mbox {(for}} | x |> | a | {\ mbox {)}}}

\int {\frac {x\;\mathrm {d} x}{\sqrt {x^{2}-a^{2}}}}={\sqrt {x^{2}-a^{2}}}\qquad {\mbox{(per }}|x|>|a|{\mbox{)}}

{\ displaystyle \ int {\ frac {x \; \ mathrm {d} x} {\ sqrt {x ^ {2} -a ^ {2}}}} = {\ sqrt {x ^ {2} -a ^ {2}}} \ qquad {\ mbox {(for}} | x |> | a | {\ mbox {)}}}

{\ displaystyle \ int {\ frac {x \; \ mathrm {d} x} {\ sqrt {x ^ {2} -a ^ {2}}}} = {\ sqrt {x ^ {2} -a ^ {2}}} \ qquad {\ mbox {(for}} | x |> | a | {\ mbox {)}}}

\int {\frac {x^{2}\,\mathrm {d} x}{\sqrt {x^{2}-a^{2}}}}={\frac {x}{2}}{\sqrt {x^{2}-a^{2}}}+{\frac {a^{2}}{2}}\,\mathrm {arcosh} \left|{\frac {x}{a}}\right|={\frac {1}{2}}\left(x{\sqrt {x^{2}-a^{2}}}+a^{2}\ln \left(|x|+{\sqrt {x^{2}-a^{2}}}\right)\right)\qquad {\mbox{(per }}|x|>|a|{\mbox{)}}

{\ displaystyle \ int {\ frac {x ^ {2} \, \ mathrm {d} x} {\ sqrt {x ^ {2} -a ^ {2}}}} = {\ frac {x} {2 }} {\ sqrt {x ^ {2} -a ^ {2}}} + {\ frac {a ^ {2}} {2}} \, \ mathrm {arcosh} \ left | {\ frac {x} {a}} \ right | = {\ frac {1} {2}} \ left (x {\ sqrt {x ^ {2} -a ^ {2}}} + a ^ {2} \ ln \ left ( | x | + {\ sqrt {x ^ {2} -a ^ {2}}} \ right) \ right) \ qquad {\ mbox {(per}} | x |> | a | {\ mbox {)} }}

{\ displaystyle \ int {\ frac {x ^ {2} \, \ mathrm {d} x} {\ sqrt {x ^ {2} -a ^ {2}}}} = {\ frac {x} {2 }} {\ sqrt {x ^ {2} -a ^ {2}}} + {\ frac {a ^ {2}} {2}} \, \ mathrm {arcosh} \ left | {\ frac {x} {a}} \ right | = {\ frac {1} {2}} \ left (x {\ sqrt {x ^ {2} -a ^ {2}}} + a ^ {2} \ ln \ left ( | x | + {\ sqrt {x ^ {2} -a ^ {2}}} \ right) \ right) \ qquad {\ mbox {(per}} | x |> | a | {\ mbox {)} }}

\int {\frac {\mathrm {d} x}{\sqrt {ax^{2}+bx+c}}}={\frac {1}{\sqrt {a}}}\ln \left|2{\sqrt {a(ax^{2}+bx+c)}}+2ax+b\right|\qquad {\mbox{(per }}a>0{\mbox{)}}

{\ displaystyle \ int {\ frac {\ mathrm {d} x} {\ sqrt {ax ^ {2} + bx + c}}} = {\ frac {1} {\ sqrt {a}}} \ ln \ left | 2 {\ sqrt {a (ax ^ {2} + bx + c)}} + 2ax + b \ right | \ qquad {\ mbox {(for}} a> 0 {\ mbox {)}}}

{\ displaystyle \ int {\ frac {\ mathrm {d} x} {\ sqrt {ax ^ {2} + bx + c}}} = {\ frac {1} {\ sqrt {a}}} \ ln \ left | 2 {\ sqrt {a (ax ^ {2} + bx + c)}} + 2ax + b \ right | \ qquad {\ mbox {(for}} a> 0 {\ mbox {)}}}

\int {\frac {\mathrm {d} x}{\sqrt {ax^{2}+bx+c}}}={\frac {1}{\sqrt {a}}}\,\mathrm {arsinh} {\frac {2ax+b}{\sqrt {4ac-b^{2}}}}\qquad {\mbox{(per }}a>0{\mbox{, }}4ac-b^{2}>0{\mbox{)}}

{\ displaystyle \ int {\ frac {\ mathrm {d} x} {\ sqrt {ax ^ {2} + bx + c}}} = {\ frac {1} {\ sqrt {a}}} \, \ mathrm {arsinh} {\ frac {2ax + b} {\ sqrt {4ac-b ^ {2}}}} \ qquad {\ mbox {(per}} a> 0 {\ mbox {,}} 4ac-b ^ {2}> 0 {\ mbox {)}}}

{\ displaystyle \ int {\ frac {\ mathrm {d} x} {\ sqrt {ax ^ {2} + bx + c}}} = {\ frac {1} {\ sqrt {a}}} \, \ mathrm {arsinh} {\ frac {2ax + b} {\ sqrt {4ac-b ^ {2}}}} \ qquad {\ mbox {(per}} a> 0 {\ mbox {,}} 4ac-b ^ {2}> 0 {\ mbox {)}}}

\int {\frac {\mathrm {d} x}{\sqrt {ax^{2}+bx+c}}}={\frac {1}{\sqrt {a}}}\log |2ax+b|\qquad {\mbox{(per }}a>0{\mbox{, }}4ac-b^{2}=0{\mbox{)}}

{\ displaystyle \ int {\ frac {\ mathrm {d} x} {\ sqrt {ax ^ {2} + bx + c}}} = {\ frac {1} {\ sqrt {a}}} \ log | 2ax + b | \ qquad {\ mbox {(pentru}} a> 0 {\ mbox {,}} 4ac-b ^ {2} = 0 {\ mbox {)}}}

{\ displaystyle \ int {\ frac {\ mathrm {d} x} {\ sqrt {ax ^ {2} + bx + c}}} = {\ frac {1} {\ sqrt {a}}} \ log | 2ax + b | \ qquad {\ mbox {(pentru}} a> 0 {\ mbox {,}} 4ac-b ^ {2} = 0 {\ mbox {)}}}

\int {\frac {\mathrm {d} x}{\sqrt {ax^{2}+bx+c}}}=-{\frac {1}{\sqrt {-a}}}\arcsin {\frac {2ax+b}{\sqrt {b^{2}-4ac}}}\qquad {\mbox{(per }}a<0{\mbox{, }}4ac-b^{2}<0{\mbox{)}}

{\ displaystyle \ int {\ frac {\ mathrm {d} x} {\ sqrt {ax ^ {2} + bx + c}}} = - {\ frac {1} {\ sqrt {-a}}} \ arcsin {\ frac {2ax + b} {\ sqrt {b ^ {2} -4ac}}} \ qquad {\ mbox {(per}} a <0 {\ mbox {,}} 4ac-b ^ {2} <0 {\ mbox {)}}}

{\ displaystyle \ int {\ frac {\ mathrm {d} x} {\ sqrt {ax ^ {2} + bx + c}}} = - {\ frac {1} {\ sqrt {-a}}} \ arcsin {\ frac {2ax + b} {\ sqrt {b ^ {2} -4ac}}} \ qquad {\ mbox {(per}} a <0 {\ mbox {,}} 4ac-b ^ {2} <0 {\ mbox {)}}}

\int {\frac {x\;\mathrm {d} x}{\sqrt {ax^{2}+bx+c}}}={\frac {\sqrt {ax^{2}+bx+c}}{a}}-{\frac {b}{2a}}\int {\frac {\mathrm {d} x}{\sqrt {ax^{2}+bx+c}}}

{\ displaystyle \ int {\ frac {x \; \ mathrm {d} x} {\ sqrt {ax ^ {2} + bx + c}}} = {\ frac {\ sqrt {ax ^ {2} + bx + c}} {a}} - {\ frac {b} {2a}} \ int {\ frac {\ mathrm {d} x} {\ sqrt {ax ^ {2} + bx + c}}}}

{\ displaystyle \ int {\ frac {x \; \ mathrm {d} x} {\ sqrt {ax ^ {2} + bx + c}}} = {\ frac {\ sqrt {ax ^ {2} + bx + c}} {a}} - {\ frac {b} {2a}} \ int {\ frac {\ mathrm {d} x} {\ sqrt {ax ^ {2} + bx + c}}}}

Bibliografie

Murray R. Spiegel, Manual de matematică , Etas Libri, 1974, pp. 61-73.

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