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

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

Apply u-substitution

: \int v d v

= \int v d v

Apply the Power Rule

: \frac{v ^{2}}{2}

= \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

x - cos (5 y) = 0

\int_{0}^{π} 19 sin^{2} (2 x) d x

x \to 0 lim (ln (2 x))

ln (\frac{x ^{2} ( x ^{3} + 1 )}{e ^{2 x}})

\frac{d}{d x} (4 + x - 7)

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