What is the integral of csch^2(1-x^2)x ?

The integral of csch^2(1-x^2)x is 1/2 coth(1-x^2)+C

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integral of csch^2(1-x^2)x

\int csch^{2} (1 - x^{2}) x d x

\frac{1}{2} coth (1 - x^{2}) + C

Solution steps

\int csch^{2} (1 - x^{2}) x d x

Apply u-substitution

: \int - \frac{csch ^{2} ( u )}{2} d u

= \int - \frac{csch ^{2} ( u )}{2} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \frac{1}{2} \cdot \int csch^{2} (u) d u

Use the common integral:

\int csch^{2} (u) d u = - coth (u)

= - \frac{1}{2} (- coth (u))

Substitute back

u = 1 - x^{2}

= - \frac{1}{2} (- coth (1 - x^{2}))

Simplify

= \frac{1}{2} coth (1 - x^{2})

Add a constant to the solution

= \frac{1}{2} coth (1 - x^{2}) + C

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What is the integral of csch^2(1-x^2)x ?
The integral of csch^2(1-x^2)x is 1/2 coth(1-x^2)+C