What is the integral of (cot^3(x))/4 ?

The integral of (cot^3(x))/4 is 1/4 (-(cot^2(x))/2-ln|sin(x)|)+C

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integral of (cot^3(x))/4

\int \frac{cot ^{3} ( x )}{4} d x

\frac{1}{4} (- \frac{cot ^{2} ( x )}{2} - ln ∣ sin (x) ∣) + C

Solution steps

\int \frac{cot ^{3} ( x )}{4} d x

Take the constant out:

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

= \frac{1}{4} \cdot \int cot^{3} (x) d x

Apply Integral Reduction

= \frac{1}{4} (- \frac{cot ^{2} ( x )}{2} - \int cot (x) d x)

\int cot (x) d x = ln ∣ sin (x) ∣

= \frac{1}{4} (- \frac{cot ^{2} ( x )}{2} - ln ∣ sin (x) ∣)

Add a constant to the solution

= \frac{1}{4} (- \frac{cot ^{2} ( x )}{2} - ln ∣ sin (x) ∣) + C

\int \frac{1}{a - x} d x

\int (- 16 tan (x) cos (x)) d x

\int \frac{e ^{- 2 x}}{x ^{2} e ^{- 2 x}} d x

\int \frac{1 + x ^{4}}{x ^{3} + x} d x

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

What is the integral of (cot^3(x))/4 ?
The integral of (cot^3(x))/4 is 1/4 (-(cot^2(x))/2-ln|sin(x)|)+C