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

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

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integral of cot^3(y)

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

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

Solution steps

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

Apply Integral Reduction

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

\int cot (y) d y = ln ∣ sin (y) ∣

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

Add a constant to the solution

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

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