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

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

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

\int (e^{c o s (x)} sin (x)) d x

- e^{c o s (x)} + C

Solution steps

\int e^{c o s (x)} sin (x) d x

Apply u-substitution

: \int - e^{u} d u

= \int - e^{u} d u

Take the constant out:

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

= - \int e^{u} d u

Use the common integral:

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

= - e^{u}

Substitute back

u = cos (x)

= - e^{c o s (x)}

Add a constant to the solution

= - e^{c o s (x)} + C

x \to 0 lim (ln (x^{2}) 2 e^{x} + 1)

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

\int \frac{r ^{4}}{4 + r ^{2}} d r

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\int_{0}^{1} \frac{x - 5}{x ^{2} - 5 x + 6} d x

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