What is the integral of (sinh(x))/(1+sinh^2(x)) ?

The integral of (sinh(x))/(1+sinh^2(x)) is sinh(x)tanh(x)-cosh(x)+C

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integral of (sinh(x))/(1+sinh^2(x))

\int \frac{sinh ( x )}{1 + sinh ^{2} ( x )} d x

sinh (x) tanh (x) - cosh (x) + C

Solution steps

\int \frac{sinh ( x )}{1 + sinh ^{2} ( x )} d x

Rewrite using trig identities

= \int \frac{sinh ( x )}{cosh ^{2} ( x )} d x

Apply Integration By Parts

= sinh (x) tanh (x) - \int cosh (x) tanh (x) d x

\int cosh (x) tanh (x) d x = cosh (x)

= sinh (x) tanh (x) - cosh (x)

Add a constant to the solution

= sinh (x) tanh (x) - cosh (x) + C

What is the integral of (sinh(x))/(1+sinh^2(x)) ?
The integral of (sinh(x))/(1+sinh^2(x)) is sinh(x)tanh(x)-cosh(x)+C