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

The integral of x^2+1/(x^2) is (x^3)/3-1/x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

\frac{x ^{3}}{3} - \frac{1}{x} + C

Solution steps

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

\int x^{2} d x = \frac{x ^{3}}{3}

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

= \frac{x ^{3}}{3} - \frac{1}{x}

Add a constant to the solution

= \frac{x ^{3}}{3} - \frac{1}{x} + C

\int (x + 1) sin (5 x) d x

\frac{d y}{d x} = \frac{cos ( 20 x )}{e ^{20 y}}, y (0) = 2

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

\int \frac{cot ( \frac{x}{2} )}{sin ( x )} d x

f (x) = 8 (4 e^{x} - 26)^{4}

What is the integral of x^2+1/(x^2) ?
The integral of x^2+1/(x^2) is (x^3)/3-1/x+C