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

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

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integral of cos(x)*cos(2x)

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

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

Solution steps

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

Apply Integration By Parts

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

= 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)

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

Simplify

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

Add a constant to the solution

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

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