What is the integral of sin(3x)sin^2(4x) ?

The integral of sin(3x)sin^2(4x) is -1/3 sin^2(4x)cos(3x)+2/165 (-5cos(11x)-11cos(5x))+C

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integral of sin(3x)sin^2(4x)

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

- \frac{1}{3} sin^{2} (4 x) cos (3 x) + \frac{2}{165} (- 5 cos (11 x) - 11 cos (5 x)) + C

Solution steps

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

Apply Integration By Parts

: - \frac{1}{3} sin^{2} (4 x) cos (3 x) - \int - \frac{4}{3} sin (8 x) cos (3 x) d x

= - \frac{1}{3} sin^{2} (4 x) cos (3 x) - \int - \frac{4}{3} sin (8 x) cos (3 x) d x

\int - \frac{4}{3} sin (8 x) cos (3 x) d x = - \frac{2}{165} (- 5 cos (11 x) - 11 cos (5 x))

= - \frac{1}{3} sin^{2} (4 x) cos (3 x) - (- \frac{2}{165} (- 5 cos (11 x) - 11 cos (5 x)))

Simplify

= - \frac{1}{3} sin^{2} (4 x) cos (3 x) + \frac{2}{165} (- 5 cos (11 x) - 11 cos (5 x))

Add a constant to the solution

= - \frac{1}{3} sin^{2} (4 x) cos (3 x) + \frac{2}{165} (- 5 cos (11 x) - 11 cos (5 x)) + C

\frac{\partial}{\partial x} (ln (9 x^{2} + 5 y^{2}))

\frac{2 s + 1}{s ^{2} + 2 s + 2}

\frac{\partial}{\partial z} (cos (y) sin (x))

ln (x y)

y = x^{3} - 13 x, (1, - 12)

What is the integral of sin(3x)sin^2(4x) ?
The integral of sin(3x)sin^2(4x) is -1/3 sin^2(4x)cos(3x)+2/165 (-5cos(11x)-11cos(5x))+C