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{3 d y}{d x} + 15 y = 90, y (0) = 0

\int (2 sin (x) - \frac{π}{4} x) d x

\frac{d}{d x} (ln (\frac{x}{x}))

\frac{d}{d t} (a cos^{3} (t))

f (x) = x^{2} + 21, at x = 2

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