What is the integral of 9cot^4(x) ?

The integral of 9cot^4(x) is 9(-1/3 cot^3(x)+x+cot(x))+C

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integral of 9cot^4(x)

\int 9 cot^{4} (x) d x

9 (- \frac{1}{3} cot^{3} (x) + x + cot (x)) + C

Solution steps

\int 9 cot^{4} (x) d x

Take the constant out:

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

= 9 \cdot \int cot^{4} (x) d x

Apply Integral Reduction

= 9 (- \frac{cot ^{3} ( x )}{3} - \int cot^{2} (x) d x)

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

= 9 (- \frac{cot ^{3} ( x )}{3} - (- x - cot (x)))

Simplify

9 (- \frac{cot ^{3} ( x )}{3} - (- x - cot (x))) : 9 (- \frac{1}{3} cot^{3} (x) + x + cot (x))

= 9 (- \frac{1}{3} cot^{3} (x) + x + cot (x))

Add a constant to the solution

= 9 (- \frac{1}{3} cot^{3} (x) + x + cot (x)) + C

What is the integral of 9cot^4(x) ?
The integral of 9cot^4(x) is 9(-1/3 cot^3(x)+x+cot(x))+C