What is the integral of 5cot^4(x) ?

The integral of 5cot^4(x) is 5(-1/3 cot^3(x)+x+cot(x))+C

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integral of 5cot^4(x)

\int 5 cot^{4} (x) d x

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

Solution steps

\int 5 cot^{4} (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^{4} (x) d x

Apply Integral Reduction

= 5 (- \frac{cot ^{3} ( x )}{3} - \int cot^{2} (x) d x)

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

= 5 (- \frac{cot ^{3} ( x )}{3} - (- x - cot (x)))

Simplify

5 (- \frac{cot ^{3} ( x )}{3} - (- x - cot (x))) : 5 (- \frac{1}{3} cot^{3} (x) + x + cot (x))

= 5 (- \frac{1}{3} cot^{3} (x) + x + cot (x))

Add a constant to the solution

= 5 (- \frac{1}{3} cot^{3} (x) + x + cot (x)) + C

\int_{1}^{2} \frac{1}{x ^{2}} - \frac{4}{x ^{3}} d x

\frac{d}{d t} (f (t))

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

\int_{- \infty}^{\infty} x d x

\int e^{- 2 x} (x^{2} - 3 x + 4) d x

What is the integral of 5cot^4(x) ?
The integral of 5cot^4(x) is 5(-1/3 cot^3(x)+x+cot(x))+C