What is the integral of x^{-2}(2x^4+3x^2-2x^{-3}) ?

The integral of x^{-2}(2x^4+3x^2-2x^{-3}) is -(2x^7+3x^5-2}{x^4}+\frac{8x^3)/3+6x-3/(2x^4)+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}(2x^4+3x^2-2x^{-3})

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

- \frac{2 x ^{7} + 3 x ^{5} - 2}{x ^{4}} + \frac{8 x ^{3}}{3} + 6 x - \frac{3}{2 x ^{4}} + C

Solution steps

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

Apply Integration By Parts

: - \frac{2 x ^{7} + 3 x ^{5} - 2}{x ^{4}} - \int - \frac{8 x ^{7} + 6 x ^{5} + 6}{x ^{5}} d x

= - \frac{2 x ^{7} + 3 x ^{5} - 2}{x ^{4}} - \int - \frac{8 x ^{7} + 6 x ^{5} + 6}{x ^{5}} d x

\int - \frac{8 x ^{7} + 6 x ^{5} + 6}{x ^{5}} d x = - \frac{8 x ^{3}}{3} - 6 x + \frac{3}{2 x ^{4}}

= - \frac{2 x ^{7} + 3 x ^{5} - 2}{x ^{4}} - (- \frac{8 x ^{3}}{3} - 6 x + \frac{3}{2 x ^{4}})

Simplify

= - \frac{2 x ^{7} + 3 x ^{5} - 2}{x ^{4}} + \frac{8 x ^{3}}{3} + 6 x - \frac{3}{2 x ^{4}}

Add a constant to the solution

= - \frac{2 x ^{7} + 3 x ^{5} - 2}{x ^{4}} + \frac{8 x ^{3}}{3} + 6 x - \frac{3}{2 x ^{4}} + C

\int \frac{x}{3 - 2 x} d x

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

\int \frac{6}{25 - ( x + 5 ) ^{2}} d x

\int (7 - 2 x)^{10} d x

\int \frac{( x ^{4} )}{x ^{2} + 1} d x

What is the integral of x^{-2}(2x^4+3x^2-2x^{-3}) ?
The integral of x^{-2}(2x^4+3x^2-2x^{-3}) is -(2x^7+3x^5-2}{x^4}+\frac{8x^3)/3+6x-3/(2x^4)+C