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

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

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integral of (sin^3(e^x))(cos(e^x))e^x

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

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

Solution steps

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

Apply u-substitution

: \int sin^{3} (u) cos (u) d u

= \int sin^{3} (u) cos (u) 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{sin ^{4} ( e ^{x} )}{4}

Add a constant to the solution

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

\int x^{2} - \frac{3}{x} + cos (x) - \frac{2}{x} d x

\int_{- 2}^{1} x^{- 4} d x

\int \frac{1}{( 1 + 5 x ) 5 x} d x

\frac{d}{d x} (\frac{3}{x ^{2}} - \frac{4}{x ^{3}})

\int_{0}^{1} \frac{ln ( x )}{5 x} d x

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