What is the integral of e^{3cos(2x)}sin(2x) ?

The integral of e^{3cos(2x)}sin(2x) is -1/6 e^{3cos(2x)}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of e^{3cos(2x)}sin(2x)

\int e^{3 c o s (2 x)} sin (2 x) d x

- \frac{1}{6} e^{3 c o s (2 x)} + C

Solution steps

\int e^{3 c o s (2 x)} sin (2 x) d x

Apply u-substitution

= \int - \frac{e ^{u}}{6} d u

Take the constant out:

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

= - \frac{1}{6} \cdot \int e^{u} d u

Use the common integral:

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

= - \frac{1}{6} e^{u}

Substitute back

u = 3 cos (2 x)

= - \frac{1}{6} e^{3 c o s (2 x)}

Add a constant to the solution

= - \frac{1}{6} e^{3 c o s (2 x)} + C

What is the integral of e^{3cos(2x)}sin(2x) ?
The integral of e^{3cos(2x)}sin(2x) is -1/6 e^{3cos(2x)}+C