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

The integral of (sin(x))/(e^{cos(x))} is 1/(e^{cos(x))}+C

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

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

\frac{1}{e ^{c o s (x)}} + C

Solution steps

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

Apply u-substitution

: \int - \frac{1}{e ^{u}} d u

= \int - \frac{1}{e ^{u}} d u

Take the constant out:

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

= - \int \frac{1}{e ^{u}} d u

Apply u-substitution

: \int \frac{1}{v ^{2}} d v

= - \int \frac{1}{v ^{2}} d v

Apply the Power Rule

: - \frac{1}{v}

= - (- \frac{1}{v})

Substitute back

= - (- \frac{1}{e ^{c o s (x)}})

Simplify

= \frac{1}{e ^{c o s (x)}}

Add a constant to the solution

= \frac{1}{e ^{c o s (x)}} + C

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What is the integral of (sin(x))/(e^{cos(x))} ?
The integral of (sin(x))/(e^{cos(x))} is 1/(e^{cos(x))}+C