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

= \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 = - sin (x)

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

Add a constant to the solution

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

x \to 0 - lim (1 - \frac{3}{x} + \frac{1}{x ^{2}})

y = (1 + 4 x)^{\frac{3}{2}}

\int x sin (\frac{nπ x}{3}) d x

\frac{1}{s ^{2} ( s ^{2} + 1 ^{2} )}

\int x \cdot arctan (x) 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