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

The integral of cos^2(x)cos(2x) is 1/2 cos^2(x)sin(2x)+1/4 (x-1/4 sin(4x))+C

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integral of cos^2(x)cos(2x)

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

\frac{1}{2} cos^{2} (x) sin (2 x) + \frac{1}{4} (x - \frac{1}{4} sin (4 x)) + C

Solution steps

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

Apply Integration By Parts

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

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

\int - \frac{1}{2} sin^{2} (2 x) d x = - \frac{1}{4} (x - \frac{1}{4} sin (4 x))

= \frac{1}{2} cos^{2} (x) sin (2 x) - (- \frac{1}{4} (x - \frac{1}{4} sin (4 x)))

Simplify

= \frac{1}{2} cos^{2} (x) sin (2 x) + \frac{1}{4} (x - \frac{1}{4} sin (4 x))

Add a constant to the solution

= \frac{1}{2} cos^{2} (x) sin (2 x) + \frac{1}{4} (x - \frac{1}{4} sin (4 x)) + C

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What is the integral of cos^2(x)cos(2x) ?
The integral of cos^2(x)cos(2x) is 1/2 cos^2(x)sin(2x)+1/4 (x-1/4 sin(4x))+C