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

The integral of sin^2(x)cos(x)ln(sin(x)) is 1/3 sin^3(x)ln(sin(x))-1/9 sin^3(x)+C

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

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

\frac{1}{3} sin^{3} (x) ln (sin (x)) - \frac{1}{9} sin^{3} (x) + C

Solution steps

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

Apply Integration By Parts

: \frac{1}{3} sin^{3} (x) ln (sin (x)) - \int \frac{1}{3} sin^{3} (x) cot (x) d x

= \frac{1}{3} sin^{3} (x) ln (sin (x)) - \int \frac{1}{3} sin^{3} (x) cot (x) d x

\int \frac{1}{3} sin^{3} (x) cot (x) d x = \frac{1}{9} sin^{3} (x)

= \frac{1}{3} sin^{3} (x) ln (sin (x)) - \frac{1}{9} sin^{3} (x)

Add a constant to the solution

= \frac{1}{3} sin^{3} (x) ln (sin (x)) - \frac{1}{9} sin^{3} (x) + C

\int sin^{5} (x) \cdot cos^{2} (x) d x

\frac{d}{d x} (x^{3} - 2 x + 1)

\frac{\partial}{\partial x} (2 tan (x y))

y^{^{'}} + a y = 0

\frac{d}{d x} (3 x^{e})

What is the integral of sin^2(x)cos(x)ln(sin(x)) ?
The integral of sin^2(x)cos(x)ln(sin(x)) is 1/3 sin^3(x)ln(sin(x))-1/9 sin^3(x)+C