What is the integral of csch^2(θ)e^{coth(θ)} ?

The integral of csch^2(θ)e^{coth(θ)} is -e^{coth(θ)}+C

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integral of csch^2(θ)e^{coth(θ)}

\int csch^{2} (θ) e^{c o t h (θ)} d θ

- e^{c o t h (θ)} + C

Solution steps

\int csch^{2} (θ) e^{c o t h (θ)} d θ

Apply u-substitution

= \int - 1 d u

Integral of a constant:

\int a d x = a x

= (- 1) u

Substitute back

u = e^{c o t h (θ)}

= (- 1) e^{c o t h (θ)}

Simplify

= - e^{c o t h (θ)}

Add a constant to the solution

= - e^{c o t h (θ)} + C

What is the integral of csch^2(θ)e^{coth(θ)} ?
The integral of csch^2(θ)e^{coth(θ)} is -e^{coth(θ)}+C