What is the integral of 1/((1+x^2)(1+arctan(x))) ?

The integral of 1/((1+x^2)(1+arctan(x))) is ln|1+arctan(x)|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 1/((1+x^2)(1+arctan(x)))

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

ln ∣ 1 + arctan (x) ∣ + C

Solution steps

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

Apply u-substitution

= \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = 1 + arctan (x)

= ln ∣ 1 + arctan (x) ∣

Add a constant to the solution

= ln ∣ 1 + arctan (x) ∣ + C

What is the integral of 1/((1+x^2)(1+arctan(x))) ?
The integral of 1/((1+x^2)(1+arctan(x))) is ln|1+arctan(x)|+C