What is the integral of 7sin^2(x)cos(x)ln(sin(x)) ?

The integral of 7sin^2(x)cos(x)ln(sin(x)) is 7(1/3 sin^3(x)ln(sin(x))-1/9 sin^3(x))+C

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integral of 7sin^2(x)cos(x)ln(sin(x))

\int 7 sin^{2} (x) cos (x) ln (sin (x)) d x

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

Solution steps

\int 7 sin^{2} (x) cos (x) ln (sin (x)) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 7 \cdot \int sin^{2} (x) cos (x) ln (sin (x)) d x

Apply Integration By Parts

= 7 (\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)

= 7 (\frac{1}{3} sin^{3} (x) ln (sin (x)) - \frac{1}{9} sin^{3} (x))

Add a constant to the solution

= 7 (\frac{1}{3} sin^{3} (x) ln (sin (x)) - \frac{1}{9} sin^{3} (x)) + C

What is the integral of 7sin^2(x)cos(x)ln(sin(x)) ?
The integral of 7sin^2(x)cos(x)ln(sin(x)) is 7(1/3 sin^3(x)ln(sin(x))-1/9 sin^3(x))+C