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

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

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

arctan (e^{x}) + C

Solution steps

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

Apply u-substitution

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

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

Use the common integral:

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

= arctan (u)

Substitute back

u = e^{x}

= arctan (e^{x})

Add a constant to the solution

= arctan (e^{x}) + C

y^{^{'}} + a \cdot y = b

\frac{d}{d x} (2 x + 2 (cos (x) + 1) sin (x))

\int sec^{6} (3 x) tan^{2} (3 x) d x

f (x) = \frac{1 + 4 x}{9 - 6 x}

\int - x^{2} + 5 x d x

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