What is the integral of (5+sin(x))^3cos(x) ?

The integral of (5+sin(x))^3cos(x) is ((5+sin(x))^4)/4+C

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integral of (5+sin(x))^3cos(x)

\int (5 + sin (x))^{3} cos (x) d x

\frac{( 5 + sin ( x ) ) ^{4}}{4} + C

Solution steps

\int (5 + sin (x))^{3} cos (x) d x

Apply u-substitution

: \int (5 + u)^{3} d u

= \int (5 + 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{( 5 + sin ( x ) ) ^{4}}{4}

Add a constant to the solution

= \frac{( 5 + sin ( x ) ) ^{4}}{4} + C

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What is the integral of (5+sin(x))^3cos(x) ?
The integral of (5+sin(x))^3cos(x) is ((5+sin(x))^4)/4+C