What is the integral of (1+cos(θ))^3sin(θ) ?

The integral of (1+cos(θ))^3sin(θ) is -((1+cos(θ))^4)/4+C

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integral of (1+cos(θ))^3sin(θ)

\int (1 + cos (θ))^{3} sin (θ) d θ

- \frac{( 1 + cos ( θ ) ) ^{4}}{4} + C

Solution steps

\int (1 + cos (θ))^{3} sin (θ) d θ

Apply u-substitution

: \int - (1 + u)^{3} d u

= \int - (1 + u)^{3} d u

Take the constant out:

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

= - \int (1 + u)^{3} d u

Apply u-substitution

: \int v^{3} d v

= - \int v^{3} d v

Apply the Power Rule

: \frac{v ^{4}}{4}

= - \frac{v ^{4}}{4}

Substitute back

= - \frac{( 1 + cos ( θ ) ) ^{4}}{4}

Add a constant to the solution

= - \frac{( 1 + cos ( θ ) ) ^{4}}{4} + C

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What is the integral of (1+cos(θ))^3sin(θ) ?
The integral of (1+cos(θ))^3sin(θ) is -((1+cos(θ))^4)/4+C