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

The integral of sin^2(b)xcos(b)x is (sin^2(b))/3 x^3cos(b)+C

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integral of sin^2(b)xcos(b)x

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

\frac{sin ^{2} ( b )}{3} x^{3} cos (b) + C

Solution steps

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

Take the constant out:

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

= sin^{2} (b) cos (b) \cdot \int xx d x

Simplify

xx : x^{2}

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

Apply the Power Rule

: \frac{x ^{3}}{3}

= sin^{2} (b) cos (b) \frac{x ^{3}}{3}

Simplify

sin^{2} (b) cos (b) \frac{x ^{3}}{3} : \frac{sin ^{2} ( b )}{3} x^{3} cos (b)

= \frac{sin ^{2} ( b )}{3} x^{3} cos (b)

Add a constant to the solution

= \frac{sin ^{2} ( b )}{3} x^{3} cos (b) + C

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What is the integral of sin^2(b)xcos(b)x ?
The integral of sin^2(b)xcos(b)x is (sin^2(b))/3 x^3cos(b)+C