What is the integral of cos(2x)os(x) ?

The integral of cos(2x)os(x) is d(cos(2x)sin(x)+4/3 sin^3(x))+C

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integral of cos(2x)os(x)

\int cos (2 x) d cos (x) d x

d (cos (2 x) sin (x) + \frac{4}{3} sin^{3} (x)) + C

Solution steps

\int cos (2 x) d cos (x) d x

Take the constant out:

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

= d \cdot \int cos (2 x) cos (x) d x

Apply Integration By Parts

: cos (2 x) sin (x) - \int - 2 sin (2 x) sin (x) d x

= d (cos (2 x) sin (x) - \int - 2 sin (2 x) sin (x) d x)

\int - 2 sin (2 x) sin (x) d x = - \frac{4}{3} sin^{3} (x)

= d (cos (2 x) sin (x) - (- \frac{4}{3} sin^{3} (x)))

Simplify

= d (cos (2 x) sin (x) + \frac{4}{3} sin^{3} (x))

Add a constant to the solution

= d (cos (2 x) sin (x) + \frac{4}{3} sin^{3} (x)) + C

\int 36 + x^{2} d x

\int \frac{x ^{4} - 1}{x ^{2}} d x

\int \frac{2 x + 4}{x ^{2} + 4 x + 5} d x

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

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

What is the integral of cos(2x)os(x) ?
The integral of cos(2x)os(x) is d(cos(2x)sin(x)+4/3 sin^3(x))+C