What is the integral of sec^2(x)e^{6tan(x)} ?

The integral of sec^2(x)e^{6tan(x)} is 1/6 e^{6tan(x)}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of sec^2(x)e^{6tan(x)}

\int sec^{2} (x) e^{6 t a n (x)} d x

\frac{1}{6} e^{6 t a n (x)} + C

Solution steps

\int sec^{2} (x) e^{6 t a n (x)} d x

Apply u-substitution

= \int e^{6 u} d u

Apply u-substitution

= \int e^{v} \frac{1}{6} d v

Take the constant out:

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

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

Use the common integral:

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

= \frac{1}{6} e^{v}

Substitute back

= \frac{1}{6} e^{6 t a n (x)}

Add a constant to the solution

= \frac{1}{6} e^{6 t a n (x)} + C

What is the integral of sec^2(x)e^{6tan(x)} ?
The integral of sec^2(x)e^{6tan(x)} is 1/6 e^{6tan(x)}+C