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

\frac{1}{s ^{2} ( s + 1 )}

\int \frac{t ^{3}}{t ^{2} + 9} d t

y^{^{'''}} - y^{^{''}} + 4 y^{^{'}} - 4 y = 0

\frac{d}{d x} (\frac{x - 2}{x + 2})

x \to - 2 lim (\frac{∣ x + 2 ∣}{x})

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