# figuring out a rule..

• September 28th 2009, 10:26 PM
Prodigga
figuring out a rule..
∫1/(x^(3/2)) = -2/sqrt(x) ???

im trying to figure out the rule here. its poping up a few times. these 2 questions especially:

Wolfram|Alpha

(click on "show steps" and look at step 3)

or here

Wolfram|Alpha

(sort of the same question really).

whats going on there? can someone show the working out to me for how we end up with the answer?
• September 28th 2009, 10:40 PM
mr fantastic
Quote:

Originally Posted by Prodigga
∫1/(x^(3/2)) = -2/sqrt(x) ???

[snip]

You're expected to know the rule $\int x^n \, dx = \frac{1}{n+1} x^{n+1} + C$ where $n \neq -1$. In the above integral $n = - \frac{3}{2}$.

(You are also expected to be fluent enough with basic index laws to know that $x^{-1/2} = \frac{1}{x^{1/2}} = \frac{1}{\sqrt{x}}$).