What is the integral of cos^{(3)}(5x)sin^{-2}(5x) ?

The integral of cos^{(3)}(5x)sin^{-2}(5x) is -1/5 cos^3(5x)cot(5x)-3/5 sin(5x)+1/5 sin^3(5x)+C

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integral of cos^{(3)}(5x)sin^{-2}(5x)

\int cos^{(3)} (5 x) sin^{- 2} (5 x) d x

- \frac{1}{5} cos^{3} (5 x) cot (5 x) - \frac{3}{5} sin (5 x) + \frac{1}{5} sin^{3} (5 x) + C

Solution steps

\int cos^{3} (5 x) sin^{- 2} (5 x) d x

Apply Integration By Parts

: - \frac{1}{5} cos^{3} (5 x) cot (5 x) - \int 3 cos^{2} (5 x) sin (5 x) cot (5 x) d x

= - \frac{1}{5} cos^{3} (5 x) cot (5 x) - \int 3 cos^{2} (5 x) sin (5 x) cot (5 x) d x

\int 3 cos^{2} (5 x) sin (5 x) cot (5 x) d x = \frac{3}{5} sin (5 x) - \frac{1}{5} sin^{3} (5 x)

= - \frac{1}{5} cos^{3} (5 x) cot (5 x) - (\frac{3}{5} sin (5 x) - \frac{1}{5} sin^{3} (5 x))

Simplify

= - \frac{1}{5} cos^{3} (5 x) cot (5 x) - \frac{3}{5} sin (5 x) + \frac{1}{5} sin^{3} (5 x)

Add a constant to the solution

= - \frac{1}{5} cos^{3} (5 x) cot (5 x) - \frac{3}{5} sin (5 x) + \frac{1}{5} sin^{3} (5 x) + C

\frac{\partial}{\partial x} (e^{x^{5}})

\frac{\partial}{\partial x} (\frac{x}{( 1 - x ) ^{2}})

\frac{\partial}{\partial y} (\frac{1}{x ^{3} - y ^{2}})

f (x) = x^{2} + 3, at x = 1

x \to - 10 - lim (\frac{x + 9}{x + 10})

What is the integral of cos^{(3)}(5x)sin^{-2}(5x) ?
The integral of cos^{(3)}(5x)sin^{-2}(5x) is -1/5 cos^3(5x)cot(5x)-3/5 sin(5x)+1/5 sin^3(5x)+C