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

f (x) = x + 8, (8, 4)

\int \frac{2 x}{9 - 4 x ^{2}} d x

\frac{12}{0.5 s ^{2} + 4 s + 5}

\int (x - 3) d x

\int_{0}^{\frac{1}{2}} 2 arcsin (2 y) d y

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