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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

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

Solution steps

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

Use the basic trigonometric identity:

\frac{1}{csc ( x )} = sin (x)

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

Apply u-substitution

= \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

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