Tabel cu integrale nedeterminate ale funcțiilor zonei

Această pagină conține un tabel de integrale nedeterminate ale funcțiilor zonei . Pentru alte integrale a se vedea Integral § Tabelele de integrale .

\int \mathrm {settsinh} \,{\frac {x}{c}}\,dx=x\,\mathrm {settsinh} \,{\frac {x}{c}}-{\sqrt {x^{2}+c^{2}}}

{\ displaystyle \ int \ mathrm {settsinh} \, {\ frac {x} {c}} \, dx = x \, \ mathrm {settsinh} \, {\ frac {x} {c}} - {\ sqrt {x ^ {2} + c ^ {2}}}}

{\ displaystyle \ int \ mathrm {settsinh} \, {\ frac {x} {c}} \, dx = x \, \ mathrm {settsinh} \, {\ frac {x} {c}} - {\ sqrt {x ^ {2} + c ^ {2}}}}

\int \mathrm {settcosh} \,{\frac {x}{c}}\,dx=x\,\mathrm {settcosh} \,{\frac {x}{c}}-{\sqrt {x^{2}-c^{2}}}

{\ displaystyle \ int \ mathrm {settcosh} \, {\ frac {x} {c}} \, dx = x \, \ mathrm {settcosh} \, {\ frac {x} {c}} - {\ sqrt {x ^ {2} -c ^ {2}}}}

{\ displaystyle \ int \ mathrm {settcosh} \, {\ frac {x} {c}} \, dx = x \, \ mathrm {settcosh} \, {\ frac {x} {c}} - {\ sqrt {x ^ {2} -c ^ {2}}}}

\int \mathrm {settanh} \,{\frac {x}{c}}\,dx=x\,\mathrm {settanh} \,{\frac {x}{c}}+{\frac {c}{2}}\log |c^{2}-x^{2}|\qquad {\mbox{(per }}|x|<|c|{\mbox{)}}

{\ displaystyle \ int \ mathrm {settanh} \, {\ frac {x} {c}} \, dx = x \, \ mathrm {settanh} \, {\ frac {x} {c}} + {\ frac {c} {2}} \ log | c ^ {2} -x ^ {2} | \ qquad {\ mbox {(for}} | x | <| c | {\ mbox {)}}}

{\ displaystyle \ int \ mathrm {settanh} \, {\ frac {x} {c}} \, dx = x \, \ mathrm {settanh} \, {\ frac {x} {c}} + {\ frac {c} {2}} \ log | c ^ {2} -x ^ {2} | \ qquad {\ mbox {(for}} | x | <| c | {\ mbox {)}}}

\int \mathrm {settcoth} \,{\frac {x}{c}}\,dx=x\,\mathrm {settcoth} \,{\frac {x}{c}}+{\frac {c}{2}}\log |x^{2}-c^{2}|\qquad {\mbox{(per }}|x|>|c|{\mbox{)}}

{\ displaystyle \ int \ mathrm {settcoth} \, {\ frac {x} {c}} \, dx = x \, \ mathrm {settcoth} \, {\ frac {x} {c}} + {\ frac {c} {2}} \ log | x ^ {2} -c ^ {2} | \ qquad {\ mbox {(for}} | x |> | c | {\ mbox {)}}}

{\ displaystyle \ int \ mathrm {settcoth} \, {\ frac {x} {c}} \, dx = x \, \ mathrm {settcoth} \, {\ frac {x} {c}} + {\ frac {c} {2}} \ log | x ^ {2} -c ^ {2} | \ qquad {\ mbox {(for}} | x |> | c | {\ mbox {)}}}

\int \mathrm {settsech} \,{\frac {x}{c}}\,dx=x\,\mathrm {settsech} \,{\frac {x}{c}}-c\,\mathrm {arctan} \,{\frac {x\,{\sqrt {\frac {c-x}{c+x}}}}{x-c}}\qquad {\mbox{(per }}x\in \{0,\,c\}{\mbox{)}}

{\ displaystyle \ int \ mathrm {settsech} \, {\ frac {x} {c}} \, dx = x \, \ mathrm {settsech} \, {\ frac {x} {c}} - c \, \ mathrm {arctan} \, {\ frac {x \, {\ sqrt {\ frac {cx} {c + x}}} {xc}} \ qquad {\ mbox {(for}} x \ in \ {0 , \, c \} {\ mbox {)}}}

{\ displaystyle \ int \ mathrm {settsech} \, {\ frac {x} {c}} \, dx = x \, \ mathrm {settsech} \, {\ frac {x} {c}} - c \, \ mathrm {arctan} \, {\ frac {x \, {\ sqrt {\ frac {cx} {c + x}}} {xc}} \ qquad {\ mbox {(for}} x \ in \ {0 , \, c \} {\ mbox {)}}}

\int \mathrm {settcsch} \,{\frac {x}{c}}\,dx=x\,\mathrm {settcsch} \,{\frac {x}{c}}+c\,\log \,{\frac {x+{\sqrt {x^{2}+c^{2}}}}{c}}\qquad {\mbox{(per }}x\in \{0,\,c\}{\mbox{)}}

{\ displaystyle \ int \ mathrm {settcsch} \, {\ frac {x} {c}} \, dx = x \, \ mathrm {settcsch} \, {\ frac {x} {c}} + c \, \ log \, {\ frac {x + {\ sqrt {x ^ {2} + c ^ {2}}}} {c}} \ qquad {\ mbox {(for}} x \ in \ {0, \ , c \} {\ mbox {)}}}

{\ displaystyle \ int \ mathrm {settcsch} \, {\ frac {x} {c}} \, dx = x \, \ mathrm {settcsch} \, {\ frac {x} {c}} + c \, \ log \, {\ frac {x + {\ sqrt {x ^ {2} + c ^ {2}}}} {c}} \ qquad {\ mbox {(pentru}} x \ in \ {0, \ , c \} {\ mbox {)}}}

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