What is the integral of cos(x)(sin(x)+1)^2 ?

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

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integral of cos(x)(sin(x)+1)^2

\int cos (x) (sin (x) + 1)^{2} d x

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

Solution steps

\int cos (x) (sin (x) + 1)^{2} d x

Apply u-substitution

: \int u^{2} d u

= \int u^{2} d u

Apply the Power Rule

: \frac{u ^{3}}{3}

= \frac{u ^{3}}{3}

Substitute back

u = sin (x) + 1

= \frac{( sin ( x ) + 1 ) ^{3}}{3}

Add a constant to the solution

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

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