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

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

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

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

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

Solution steps

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

Apply u-substitution

: \int e^{u} d u

= \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

\frac{d}{d x} (x - \frac{1}{3} x^{3})

\int \frac{x}{x + 10} d x

\int_{0}^{x} \frac{e ^{t^{2}} - 1}{t} d t

n = 1 \sum \infty \frac{n ^{5}}{3 ^{n}}

\int sec (x) (tan (x) + cos (x)) d x

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