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

The integral of ln(1+x^2) is xln(1+x^2)-2(-arctan(x)+x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of ln(1+x^2)

integral

ln (1 + x^{2})

x ln (1 + x^{2}) - 2 (- arctan (x) + x) + C

Solution steps

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

Apply Integration By Parts

: x ln (1 + x^{2}) - \int \frac{2 x ^{2}}{1 + x ^{2}} d x

= x ln (1 + x^{2}) - \int \frac{2 x ^{2}}{1 + x ^{2}} d x

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

= x ln (1 + x^{2}) - 2 (- arctan (x) + x)

Add a constant to the solution

= x ln (1 + x^{2}) - 2 (- arctan (x) + x) + C

\frac{1}{( 2 x ^{2} + 1 )}

\frac{1}{( x ^{4} - 1 )}

\frac{1}{( x + y + z + 1 ) ^{3}}

\frac{x}{( 2 + x )}

sin (x) sec^{2} (x)

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