What is the integral of cot^3(x) ?

The integral of cot^3(x) is -(cot^2(x))/2-ln|sin(x)|+C

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integral of cot^3(x)

\int cot^{3} (x) d x

- \frac{cot ^{2} ( x )}{2} - ln ∣ sin (x) ∣ + C

Solution steps

\int cot^{3} (x) d x

Apply Integral Reduction

= - \frac{cot ^{2} ( x )}{2} - \int cot (x) d x

\int cot (x) d x = ln ∣ sin (x) ∣

= - \frac{cot ^{2} ( x )}{2} - ln ∣ sin (x) ∣

Add a constant to the solution

= - \frac{cot ^{2} ( x )}{2} - ln ∣ sin (x) ∣ + C

What is the integral of cot^3(x) ?
The integral of cot^3(x) is -(cot^2(x))/2-ln|sin(x)|+C