What is the integral of sec^2(4x)e^{tan(4x)} ?

The integral of sec^2(4x)e^{tan(4x)} is 1/4 e^{tan(4x)}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of sec^2(4x)e^{tan(4x)}

\int sec^{2} (4 x) e^{t a n (4 x)} d x

\frac{1}{4} e^{t a n (4 x)} + C

Solution steps

\int sec^{2} (4 x) e^{t a n (4 x)} d x

Apply u-substitution

= \int sec^{2} (u) e^{t a n (u)} \frac{1}{4} d u

Take the constant out:

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

= \frac{1}{4} \cdot \int sec^{2} (u) e^{t a n (u)} d u

Apply u-substitution

= \frac{1}{4} \cdot \int e^{v} d v

Use the common integral:

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

= \frac{1}{4} e^{v}

Substitute back

= \frac{1}{4} e^{t a n (4 x)}

Add a constant to the solution

= \frac{1}{4} e^{t a n (4 x)} + C

What is the integral of sec^2(4x)e^{tan(4x)} ?
The integral of sec^2(4x)e^{tan(4x)} is 1/4 e^{tan(4x)}+C