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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (4e^x)/(1+e^{2x)}

\int \frac{4 e ^{x}}{1 + e ^{2 x}} d x

4 arctan (e^{x}) + C

Solution steps

\int \frac{4 e ^{x}}{1 + e ^{2 x}} d x

Take the constant out:

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

= 4 \cdot \int \frac{e ^{x}}{1 + e ^{2 x}} d x

Apply u-substitution

: \int \frac{1}{1 + u ^{2}} d u

= 4 \cdot \int \frac{1}{1 + u ^{2}} d u

Use the common integral:

\int \frac{1}{1 + u ^{2}} d u = arctan (u)

= 4 arctan (u)

Substitute back

u = e^{x}

= 4 arctan (e^{x})

Add a constant to the solution

= 4 arctan (e^{x}) + C

\int (6 y) d y

\int \frac{x ^{7}}{2} d x

\int (9 - 4 x)^{8} d x

\int (1 + \frac{1}{x})^{3} \cdot \frac{1}{x ^{2}} d x

\int 2 x^{2} - x + 100 d x

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