What is the integral of cos^3(3x)sin^{-2}(3x) ?

The integral of cos^3(3x)sin^{-2}(3x) is -1/3 cos^3(3x)cot(3x)-sin(3x)+1/3 sin^3(3x)+C

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integral of cos^3(3x)sin^{-2}(3x)

\int cos^{3} (3 x) sin^{- 2} (3 x) d x

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

Solution steps

\int cos^{3} (3 x) sin^{- 2} (3 x) d x

Apply Integration By Parts

: - \frac{1}{3} cos^{3} (3 x) cot (3 x) - \int 3 cos^{2} (3 x) sin (3 x) cot (3 x) d x

= - \frac{1}{3} cos^{3} (3 x) cot (3 x) - \int 3 cos^{2} (3 x) sin (3 x) cot (3 x) d x

\int 3 cos^{2} (3 x) sin (3 x) cot (3 x) d x = sin (3 x) - \frac{1}{3} sin^{3} (3 x)

= - \frac{1}{3} cos^{3} (3 x) cot (3 x) - (sin (3 x) - \frac{1}{3} sin^{3} (3 x))

Simplify

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

Add a constant to the solution

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

x \to - \infty lim (19)

x \to 5 lim (9)

f (x) = x - x^{2}, at x = - 1

f (x) = 3 x^{5}

What is the integral of cos^3(3x)sin^{-2}(3x) ?
The integral of cos^3(3x)sin^{-2}(3x) is -1/3 cos^3(3x)cot(3x)-sin(3x)+1/3 sin^3(3x)+C