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

The integral of e^xsin(e^x)cos(e^x) is (sin^2(e^x))/2+C

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integral of e^xsin(e^x)cos(e^x)

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

\frac{sin ^{2} ( e ^{x} )}{2} + C

Solution steps

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

Apply u-substitution

= \int sin (u) cos (u) d u

Apply u-substitution

= \int v d v

Apply the Power Rule

= \frac{v ^{2}}{2}

Substitute back

= \frac{sin ^{2} ( e ^{x} )}{2}

Add a constant to the solution

= \frac{sin ^{2} ( e ^{x} )}{2} + C

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