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

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

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

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

sin (x) e^{s i n (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

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

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

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

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

Add a constant to the solution

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

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

\int (2 x - \frac{1}{x})^{2} d x

\int \frac{ln ( x )}{( ln ( x ) + 1 ) ^{2}} d x

\int \frac{z ^{4} - 3 z ^{2} - 4 z}{6 z} d z

\int \frac{4 x ^{2}}{9 - x ^{2}} d x

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