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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

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

Solution steps

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

Take the partial fraction of

\frac{1}{x ^{2} ( x ^{2} + 5 )} : \frac{1}{5 x ^{2}} - \frac{1}{5 ( x ^{2} + 5 )}

= \int \frac{1}{5 x ^{2}} - \frac{1}{5 ( x ^{2} + 5 )} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{1}{5 x ^{2}} d x - \int \frac{1}{5 ( x ^{2} + 5 )} d x

\int \frac{1}{5 x ^{2}} d x = - \frac{1}{5 x}

\int \frac{1}{5 ( x ^{2} + 5 )} d x = \frac{1}{5 5} arctan (\frac{x}{5})

= - \frac{1}{5 x} - \frac{1}{5 5} arctan (\frac{x}{5})

Add a constant to the solution

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

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

\int \frac{cos ( \frac{π}{x ^{21}} )}{x ^{22}} d x

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

\int \frac{5}{x ( x ^{5} + 4 )} d x

\int sin^{4} (\frac{w}{2}) cos^{2} (\frac{w}{2}) d w

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