What is the integral of (2x^{5/2}-8x^2)x^{-5/2} ?

The integral of (2x^{5/2}-8x^2)x^{-5/2} is 2x-16x^{1/2}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (2x^{5/2}-8x^2)x^{-5/2}

\int (2 x^{\frac{5}{2}} - 8 x^{2}) x^{- \frac{5}{2}} d x

2 x - 16 x^{\frac{1}{2}} + C

Solution steps

\int (2 x^{\frac{5}{2}} - 8 x^{2}) x^{- \frac{5}{2}} d x

Simplify

(2 x^{\frac{5}{2}} - 8 x^{2}) x^{- \frac{5}{2}} : \frac{2 x ^{\frac{5}{2}} - 8 x ^{2}}{x ^{\frac{5}{2}}}

= \int \frac{2 x ^{\frac{5}{2}} - 8 x ^{2}}{x ^{\frac{5}{2}}} d x

Expand

\frac{2 x ^{\frac{5}{2}} - 8 x ^{2}}{x ^{\frac{5}{2}}} : 2 - \frac{8}{x ^{\frac{1}{2}}}

= \int 2 - \frac{8}{x ^{\frac{1}{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 d x - \int \frac{8}{x ^{\frac{1}{2}}} d x

\int 2 d x = 2 x

\int \frac{8}{x ^{\frac{1}{2}}} d x = 16 x^{\frac{1}{2}}

= 2 x - 16 x^{\frac{1}{2}}

Add a constant to the solution

= 2 x - 16 x^{\frac{1}{2}} + C

\int x arcsin (π x) d x

\int + 8 x - 1 d x

\int \frac{3 x ^{2} ( x ^{3} ) ^{2}}{5 x} d x

\int \frac{cos ( θ - 1 )}{sin ^{2} ( θ - 1 )} d θ

\int (x - \frac{2}{x} - 4 e^{4 x}) d x

What is the integral of (2x^{5/2}-8x^2)x^{-5/2} ?
The integral of (2x^{5/2}-8x^2)x^{-5/2} is 2x-16x^{1/2}+C