What is the integral of (2x^2+5x^{-2}) ?

The integral of (2x^2+5x^{-2}) is (2x^3)/3-5/x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (2x^2+5x^{-2})

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

\frac{2 x ^{3}}{3} - \frac{5}{x} + C

Solution steps

\int 2 x^{2} + 5 x^{- 2} d x

5 x^{- 2} = \frac{5}{x ^{2}}

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

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

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

= \frac{2 x ^{3}}{3} - \frac{5}{x}

Add a constant to the solution

= \frac{2 x ^{3}}{3} - \frac{5}{x} + C

\int \frac{1}{1 - ( 2 x - 3 ) ^{2}} d x

\int y^{2} 1 + y^{3} d y

\int \frac{3 x ^{3} + x}{1 + x ^{4}} d x

\int 6 sin (\frac{x}{2}) d x

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

What is the integral of (2x^2+5x^{-2}) ?
The integral of (2x^2+5x^{-2}) is (2x^3)/3-5/x+C