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d −1 1
sinh x = √
dx
x2 + 1
d −1 1
cosh x = √
dx
x2 − 1
d −1 1
tanh x =
dx
1 − x2 d −1 1
csch x = −
dx
|x| √ 1 + x2 d −1 1
sech x = −
dx
x √ 1 − x2 d −1 1
coth x =
dx
1 − x2
sinh ax dx = 1
cosh ax + C
a
cosh ax dx = 1
sinh ax + C
a
tanh ax dx = 1
ln(cosh ax) + C
a
coth ax dx = 1
ln(sinh ax) + C
a
du
√
a2 + u2 = sinh−1 u
+ C
a
du
√
u2 − a2 = cosh−1 u
+ C
a
du
a2 1
=
− u2 a tanh−1 u
+ C; u
a
2 < a 2
du
a2 1
=
− u2 a coth−1 u
+ C; u
a
2 > a 2
du
u √ a2 = −1
− u2 a sech−1 u
+ C
a
du
a csch−1
u
+ C
a
u √ a2 = −1
+ u2 dx
√ 1 − x 2
π
= arcsin(x) + c = −arccos(x) + + c
2
dx
√ x 2 + 1 = arcsinh(x) + c = ln(x + x 2 + 1) + c
dx
√ x 2 − 1 = arccosh(x) + c = ln(x + x 2 − 1) + c