What is the integral of 20cot^4(x) ?

The integral of 20cot^4(x) is 20(-1/3 cot^3(x)+x+cot(x))+C

Popular >

integral of 20cot^4(x)

\int 20 cot^{4} (x) d x

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

Solution steps

\int 20 cot^{4} (x) d x

Take the constant out:

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

= 20 \cdot \int cot^{4} (x) d x

Apply Integral Reduction

= 20 (- \frac{cot ^{3} ( x )}{3} - \int cot^{2} (x) d x)

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

= 20 (- \frac{cot ^{3} ( x )}{3} - (- x - cot (x)))

Simplify

20 (- \frac{cot ^{3} ( x )}{3} - (- x - cot (x))) : 20 (- \frac{1}{3} cot^{3} (x) + x + cot (x))

= 20 (- \frac{1}{3} cot^{3} (x) + x + cot (x))

Add a constant to the solution

= 20 (- \frac{1}{3} cot^{3} (x) + x + cot (x)) + C

\frac{\partial}{\partial x} (10 x^{3} + 3 x^{2} y - 3 y^{5})

y^{^{''}} - 11 y^{^{'}} + 30 y = 20 e^{t}

\int_{0}^{2} (sin (x) + e^{x}) d x

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

\frac{d}{d x} (\frac{8 x ^{2} + 8 x + 6}{x})

What is the integral of 20cot^4(x) ?
The integral of 20cot^4(x) is 20(-1/3 cot^3(x)+x+cot(x))+C