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

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

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

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

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

Solution steps

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

Apply u-substitution

= \int e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= e^{u}

Substitute back

u = sin (x)

= e^{s i n (x)}

Add a constant to the solution

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

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

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

\int x \cdot 5^{- x^{2}} d x

\int \frac{28 t + 28}{14 t ^{2} + 28 t - 9} d t

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

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