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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of v^{-2}(2v^4+3v^2-2v^{-3})

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

\frac{\partial}{\partial x} (x^{3} + e^{y^{2}})

y^{^{'}} + y = sin (x)

x \to 5 lim (ln (\frac{x}{5}))

n = 1 \sum \infty n

f (x) = ln (4 x)

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