What is the integral of 6x^{3/2}-3x^{-3/2} ?

The integral of 6x^{3/2}-3x^{-3/2} is 12/5 x^{5/2}+6/(x^{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 6x^{3/2}-3x^{-3/2}

\int 6 x^{\frac{3}{2}} - 3 x^{- \frac{3}{2}} d x

\frac{12}{5} x^{\frac{5}{2}} + \frac{6}{x ^{\frac{1}{2}}} + C

Solution steps

\int 6 x^{\frac{3}{2}} - 3 x^{- \frac{3}{2}} d x

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

= \int 6 x^{\frac{3}{2}} - \frac{3}{x ^{\frac{3}{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 6 x^{\frac{3}{2}} d x - \int \frac{3}{x ^{\frac{3}{2}}} d x

\int 6 x^{\frac{3}{2}} d x = \frac{12}{5} x^{\frac{5}{2}}

\int \frac{3}{x ^{\frac{3}{2}}} d x = - \frac{6}{x ^{\frac{1}{2}}}

= \frac{12}{5} x^{\frac{5}{2}} - (- \frac{6}{x ^{\frac{1}{2}}})

Simplify

= \frac{12}{5} x^{\frac{5}{2}} + \frac{6}{x ^{\frac{1}{2}}}

Add a constant to the solution

= \frac{12}{5} x^{\frac{5}{2}} + \frac{6}{x ^{\frac{1}{2}}} + C

x \to 0 lim (cos (x) - 1)

\frac{3}{x ^{5}}

\int x^{3} 2 + x^{2} d x

\int (5 x + 3) (x^{2} - 9) d x

\frac{d}{d x} (x^{2} + y^{2} + x y)

What is the integral of 6x^{3/2}-3x^{-3/2} ?
The integral of 6x^{3/2}-3x^{-3/2} is 12/5 x^{5/2}+6/(x^{1/2)}+C