What is the integral of 5cot^3(x) ?

The integral of 5cot^3(x) is 5(-(cot^2(x))/2-ln|sin(x)|)+C

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integral of 5cot^3(x)

\int 5 cot^{3} (x) d x

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

Solution steps

\int 5 cot^{3} (x) d x

Take the constant out:

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

= 5 \cdot \int cot^{3} (x) d x

Apply Integral Reduction

= 5 (- \frac{cot ^{2} ( x )}{2} - \int cot (x) d x)

\int cot (x) d x = ln ∣ sin (x) ∣

= 5 (- \frac{cot ^{2} ( x )}{2} - ln ∣ sin (x) ∣)

Add a constant to the solution

= 5 (- \frac{cot ^{2} ( x )}{2} - ln ∣ sin (x) ∣) + C

What is the integral of 5cot^3(x) ?
The integral of 5cot^3(x) is 5(-(cot^2(x))/2-ln|sin(x)|)+C