What is the integral of sin^2(x)cos(x)e^{sin(x)} ?

The integral of sin^2(x)cos(x)e^{sin(x)} is sin^2(x)e^{sin(x)}-2(sin(x)e^{sin(x)}-e^{sin(x)})+C

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integral of sin^2(x)cos(x)e^{sin(x)}

\int sin^{2} (x) cos (x) e^{s i n (x)} d x

sin^{2} (x) e^{s i n (x)} - 2 (sin (x) e^{s i n (x)} - e^{s i n (x)}) + C

Solution steps

\int sin^{2} (x) cos (x) e^{s i n (x)} d x

Apply Integration By Parts

: sin^{2} (x) e^{s i n (x)} - \int sin (2 x) e^{s i n (x)} d x

= sin^{2} (x) e^{s i n (x)} - \int sin (2 x) e^{s i n (x)} d x

\int sin (2 x) e^{s i n (x)} d x = 2 (sin (x) e^{s i n (x)} - e^{s i n (x)})

= sin^{2} (x) e^{s i n (x)} - 2 (sin (x) e^{s i n (x)} - e^{s i n (x)})

Add a constant to the solution

= sin^{2} (x) e^{s i n (x)} - 2 (sin (x) e^{s i n (x)} - e^{s i n (x)}) + C

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What is the integral of sin^2(x)cos(x)e^{sin(x)} ?
The integral of sin^2(x)cos(x)e^{sin(x)} is sin^2(x)e^{sin(x)}-2(sin(x)e^{sin(x)}-e^{sin(x)})+C