What is the integral of sin^2(2x)cos(3x) ?

The integral of sin^2(2x)cos(3x) is 1/3 sin^2(2x)sin(3x)-1/21 (-sin(7x)+7sin(x))+C

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integral of sin^2(2x)cos(3x)

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

\frac{1}{3} sin^{2} (2 x) sin (3 x) - \frac{1}{21} (- sin (7 x) + 7 sin (x)) + C

Solution steps

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

Apply Integration By Parts

: \frac{1}{3} sin^{2} (2 x) sin (3 x) - \int \frac{2}{3} sin (4 x) sin (3 x) d x

= \frac{1}{3} sin^{2} (2 x) sin (3 x) - \int \frac{2}{3} sin (4 x) sin (3 x) d x

\int \frac{2}{3} sin (4 x) sin (3 x) d x = \frac{1}{21} (- sin (7 x) + 7 sin (x))

= \frac{1}{3} sin^{2} (2 x) sin (3 x) - \frac{1}{21} (- sin (7 x) + 7 sin (x))

Add a constant to the solution

= \frac{1}{3} sin^{2} (2 x) sin (3 x) - \frac{1}{21} (- sin (7 x) + 7 sin (x)) + C

\frac{\partial}{\partial x} (e^{x y} cos (x + y))

\frac{d}{d x} (b x e^{x})

\frac{\partial}{\partial x} (\frac{2 x ^{2} y}{5 + x ^{2} y ^{2}})

\frac{d}{d x} (((x^{2} + 3)^{5} + x)^{2})

ln (5 + x)

What is the integral of sin^2(2x)cos(3x) ?
The integral of sin^2(2x)cos(3x) is 1/3 sin^2(2x)sin(3x)-1/21 (-sin(7x)+7sin(x))+C