What is the integral of 17cot^4(x) ?

The integral of 17cot^4(x) is 17(-1/3 cot^3(x)+x+cot(x))+C

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integral of 17cot^4(x)

\int 17 cot^{4} (x) d x

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

Solution steps

\int 17 cot^{4} (x) d x

Take the constant out:

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

= 17 \cdot \int cot^{4} (x) d x

Apply Integral Reduction

= 17 (- \frac{cot ^{3} ( x )}{3} - \int cot^{2} (x) d x)

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

= 17 (- \frac{cot ^{3} ( x )}{3} - (- x - cot (x)))

Simplify

17 (- \frac{cot ^{3} ( x )}{3} - (- x - cot (x))) : 17 (- \frac{1}{3} cot^{3} (x) + x + cot (x))

= 17 (- \frac{1}{3} cot^{3} (x) + x + cot (x))

Add a constant to the solution

= 17 (- \frac{1}{3} cot^{3} (x) + x + cot (x)) + C

\frac{d}{d t} (e^{- 2 t} cos (3 t) + e^{- 2 t} sin (3 t))

\frac{d}{d x} (- 2 x^{5} - 3 x^{3} + 1)

x \to 2 - lim (∣ x ∣ - x)

y^{^{''}} + \frac{2 y ^{^{'}}}{x} - \frac{6 y}{x ^{2}} = 0

x \to 1 lim (1 - cos (π) x)

What is the integral of 17cot^4(x) ?
The integral of 17cot^4(x) is 17(-1/3 cot^3(x)+x+cot(x))+C