What is the integral of 15cot^4(x) ?

The integral of 15cot^4(x) is 15(-1/3 cot^3(x)+x+cot(x))+C

Popular >

integral of 15cot^4(x)

\int 15 cot^{4} (x) d x

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

Solution steps

\int 15 cot^{4} (x) d x

Take the constant out:

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

= 15 \cdot \int cot^{4} (x) d x

Apply Integral Reduction

= 15 (- \frac{cot ^{3} ( x )}{3} - \int cot^{2} (x) d x)

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

= 15 (- \frac{cot ^{3} ( x )}{3} - (- x - cot (x)))

Simplify

15 (- \frac{cot ^{3} ( x )}{3} - (- x - cot (x))) : 15 (- \frac{1}{3} cot^{3} (x) + x + cot (x))

= 15 (- \frac{1}{3} cot^{3} (x) + x + cot (x))

Add a constant to the solution

= 15 (- \frac{1}{3} cot^{3} (x) + x + cot (x)) + C

\frac{\partial}{\partial x} (- 2 y cos^{2} (x))

\frac{d y}{d x} + y = x^{2} + 1

\frac{\partial}{\partial x} (y^{2} - cos (x y))

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

f (x) = \frac{x ^{2}}{( 3 + x )}

What is the integral of 15cot^4(x) ?
The integral of 15cot^4(x) is 15(-1/3 cot^3(x)+x+cot(x))+C