What is the integral of 6cot^4(x) ?

The integral of 6cot^4(x) is 6(-1/3 cot^3(x)+x+cot(x))+C

integral of 6cot^4(x)

\int 6 cot^{4} (x) d x

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

Solution steps

\int 6 cot^{4} (x) d x

Take the constant out:

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

= 6 \cdot \int cot^{4} (x) d x

Apply Integral Reduction

= 6 (- \frac{cot ^{3} ( x )}{3} - \int cot^{2} (x) d x)

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

= 6 (- \frac{cot ^{3} ( x )}{3} - (- x - cot (x)))

Simplify

6 (- \frac{cot ^{3} ( x )}{3} - (- x - cot (x))) : 6 (- \frac{1}{3} cot^{3} (x) + x + cot (x))

= 6 (- \frac{1}{3} cot^{3} (x) + x + cot (x))

Add a constant to the solution

= 6 (- \frac{1}{3} cot^{3} (x) + x + cot (x)) + C

y^{^{''}} - 4 y = e^{- 2 x} - 2 x, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + y = \frac{3}{2} sin (x)

\int x + 1 x d x

\int \frac{sin ( 2 x )}{18 + cos ^{2} ( x )} d x

y^{^{'}} + 3 y + 5 = 0

What is the integral of 6cot^4(x) ?
The integral of 6cot^4(x) is 6(-1/3 cot^3(x)+x+cot(x))+C