What is the integral of 1/(5+2x^2) ?

The integral of 1/(5+2x^2) is 1/(sqrt(10))arctan(sqrt(2/5)x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1/(5+2x^2)

\int \frac{1}{5 + 2 x ^{2}} d x

\frac{1}{10} arctan (\frac{2}{5} x) + C

Solution steps

\int \frac{1}{5 + 2 x ^{2}} d x

Apply Integral Substitution

= \int \frac{1}{10 ( 1 + u ^{2} )} d u

Take the constant out:

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

= \frac{1}{10} \cdot \int \frac{1}{1 + u ^{2}} d u

Use the common integral:

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

= \frac{1}{10} arctan (u)

Substitute back

u = \frac{2}{5} x

= \frac{1}{10} arctan (\frac{2}{5} x)

Combine same powers :

\frac{x}{y} = \frac{x}{y}

= \frac{1}{10} arctan (\frac{2}{5} x)

Add a constant to the solution

= \frac{1}{10} arctan (\frac{2}{5} x) + C

\int (\frac{1}{4 x}) d x

\int - 2 z e^{2 x} sin (yz) + 6 x y d y

\int \frac{7 x}{( 8 - x ^{2} ) ^{3}} d x

\int \frac{4}{2 - x} d x

\int (3 x^{2}) d x

What is the integral of 1/(5+2x^2) ?
The integral of 1/(5+2x^2) is 1/(sqrt(10))arctan(sqrt(2/5)x)+C