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

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

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

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

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