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

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

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

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

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

Solution steps

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

Rewrite using trig identities

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Apply Integration By Parts

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

= 2 (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)}

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

Add a constant to the solution

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

\int 2 e^{x} + \frac{3}{x} d x

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

\int \frac{1}{( sin ( x ) cos ( x ) )} d x

\int (\frac{x ^{2}}{4})^{2} d x

\int \frac{( x + 1 )}{x ^{3} + 3 x ^{2} + 7 x + 5} d x

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