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

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

Popular >

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

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

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

Solution steps

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

Apply Integration By Parts

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

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

Add a constant to the solution

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

y^{^{'}} = \frac{6 x - 12}{x ^{2}}, y (1) = 20

\frac{d}{d b} (sec (b) \cdot csc (b) \cdot sin (b))

\int (\frac{( ln ( x ) ) ^{4}}{x}) d x

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

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

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