What is the integral of cos^3(8x)sin^{-2}(8x) ?

The integral of cos^3(8x)sin^{-2}(8x) is -1/8 cos^3(8x)cot(8x)-3/8 sin(8x)+1/8 sin^3(8x)+C

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integral of cos^3(8x)sin^{-2}(8x)

\int cos^{3} (8 x) sin^{- 2} (8 x) d x

- \frac{1}{8} cos^{3} (8 x) cot (8 x) - \frac{3}{8} sin (8 x) + \frac{1}{8} sin^{3} (8 x) + C

Solution steps

\int cos^{3} (8 x) sin^{- 2} (8 x) d x

Apply Integration By Parts

: - \frac{1}{8} cos^{3} (8 x) cot (8 x) - \int 3 cos^{2} (8 x) sin (8 x) cot (8 x) d x

= - \frac{1}{8} cos^{3} (8 x) cot (8 x) - \int 3 cos^{2} (8 x) sin (8 x) cot (8 x) d x

\int 3 cos^{2} (8 x) sin (8 x) cot (8 x) d x = \frac{3}{8} sin (8 x) - \frac{1}{8} sin^{3} (8 x)

= - \frac{1}{8} cos^{3} (8 x) cot (8 x) - (\frac{3}{8} sin (8 x) - \frac{1}{8} sin^{3} (8 x))

Simplify

= - \frac{1}{8} cos^{3} (8 x) cot (8 x) - \frac{3}{8} sin (8 x) + \frac{1}{8} sin^{3} (8 x)

Add a constant to the solution

= - \frac{1}{8} cos^{3} (8 x) cot (8 x) - \frac{3}{8} sin (8 x) + \frac{1}{8} sin^{3} (8 x) + C

y^{^{'}} = \frac{( y ^{2} + 1 )}{2 y}

\int \frac{12 x ^{2} + x + 2}{x ( x ^{2} + 1 )} d x

n = 1 \sum \infty \frac{3}{n + 1}

f (x) = sin (8 x + 4)

\int \frac{48 x ^{2}}{( x - 21 ) ( x + 7 ) ^{2}} d x

What is the integral of cos^3(8x)sin^{-2}(8x) ?
The integral of cos^3(8x)sin^{-2}(8x) is -1/8 cos^3(8x)cot(8x)-3/8 sin(8x)+1/8 sin^3(8x)+C