What is the integral of (cot^3(x))/5 ?

The integral of (cot^3(x))/5 is 1/5 (-(cot^2(x))/2-ln|sin(x)|)+C

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integral of (cot^3(x))/5

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

\frac{1}{5} (- \frac{cot ^{2} ( x )}{2} - ln ∣ sin (x) ∣) + C

Solution steps

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

Take the constant out:

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

= \frac{1}{5} \cdot \int cot^{3} (x) d x

Apply Integral Reduction

= \frac{1}{5} (- \frac{cot ^{2} ( x )}{2} - \int cot (x) d x)

\int cot (x) d x = ln ∣ sin (x) ∣

= \frac{1}{5} (- \frac{cot ^{2} ( x )}{2} - ln ∣ sin (x) ∣)

Add a constant to the solution

= \frac{1}{5} (- \frac{cot ^{2} ( x )}{2} - ln ∣ sin (x) ∣) + C

\frac{d}{d y} ((\frac{y}{8})^{4} + \frac{1}{4 y ^{2}})

x^{2} y^{^{''}} - 2 y = 0

x \to 1 lim (cos (π) x)

n = 1 \sum \infty 4 (\frac{2}{3})^{n - 1}

\int \frac{1}{x ^{3} + x} d x

What is the integral of (cot^3(x))/5 ?
The integral of (cot^3(x))/5 is 1/5 (-(cot^2(x))/2-ln|sin(x)|)+C