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

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

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

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

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

Solution steps

\int e^{s i n (x)} sin (x) cos (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 \frac{x ^{2} + 1}{x ^{2} - 2} d x

\int 8 \frac{1}{x} d x

\int (- 3 x^{2}) d x

\int 3 x + 8 d x

\int \frac{1}{x ( 1 + x ^{5} )} d x

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