What is the integral of x^2*csch(x^3+1) ?

The integral of x^2*csch(x^3+1) is 1/3 ln(tanh((x^3+1)/2))+C

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integral of x^2*csch(x^3+1)

\int x^{2} \cdot csch (x^{3} + 1) d x

\frac{1}{3} ln (tanh (\frac{x ^{3} + 1}{2})) + C

Solution steps

\int x^{2} csch (x^{3} + 1) d x

Apply u-substitution

: \int \frac{csch ( u )}{3} d u

= \int \frac{csch ( u )}{3} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int csch (u) d u

Use the common integral:

\int csch (u) d u = ln (tanh (\frac{u}{2}))

= \frac{1}{3} ln (tanh (\frac{u}{2}))

Substitute back

u = x^{3} + 1

= \frac{1}{3} ln (tanh (\frac{x ^{3} + 1}{2}))

Add a constant to the solution

= \frac{1}{3} ln (tanh (\frac{x ^{3} + 1}{2})) + C

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What is the integral of x^2*csch(x^3+1) ?
The integral of x^2*csch(x^3+1) is 1/3 ln(tanh((x^3+1)/2))+C