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

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

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

ln (2) arctan (x) + C

Solution steps

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

Take the constant out:

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

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

Use the common integral:

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

= ln (2) arctan (x)

Add a constant to the solution

= ln (2) arctan (x) + C

\int \frac{x + 1}{x + 1} d x

\int \frac{\frac{5 ( x ^{3} + 2 )}{x ^{4}}}{\frac{- 30}{x}} d x

(\frac{1}{3}) x^{3} - 5 x

\int x^{3} a^{2} - x^{2} d x

\int \frac{5 x ^{4} - 8 x ^{2} + 3 x - 2}{x ^{2}} d x

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