What is the integral of 16cot^4(x) ?

The integral of 16cot^4(x) is 16(-1/3 cot^3(x)+x+cot(x))+C

Popular >

integral of 16cot^4(x)

\int 16 cot^{4} (x) d x

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

Solution steps

\int 16 cot^{4} (x) d x

Take the constant out:

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

= 16 \cdot \int cot^{4} (x) d x

Apply Integral Reduction

= 16 (- \frac{cot ^{3} ( x )}{3} - \int cot^{2} (x) d x)

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

= 16 (- \frac{cot ^{3} ( x )}{3} - (- x - cot (x)))

Simplify

16 (- \frac{cot ^{3} ( x )}{3} - (- x - cot (x))) : 16 (- \frac{1}{3} cot^{3} (x) + x + cot (x))

= 16 (- \frac{1}{3} cot^{3} (x) + x + cot (x))

Add a constant to the solution

= 16 (- \frac{1}{3} cot^{3} (x) + x + cot (x)) + C

\int \frac{( x + 1 )}{x ^{3} + x ^{2} - 6 x} d x

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

\int ln (\frac{x}{1 + x}) d x

\frac{d}{d x} (2 x^{2} cos (x) cot (x))

\frac{d y}{d x}, x y - 8 = 0

What is the integral of 16cot^4(x) ?
The integral of 16cot^4(x) is 16(-1/3 cot^3(x)+x+cot(x))+C