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

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

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

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

arctan (cosh (x)) + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{1 + u ^{2}} d u

= \int \frac{1}{1 + u ^{2}} d u

Use the common integral:

\int \frac{1}{1 + u ^{2}} d u = arctan (u)

= arctan (u)

Substitute back

u = cosh (x)

= arctan (cosh (x))

Add a constant to the solution

= arctan (cosh (x)) + C

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