How to integrate the following ??

Question

$intdx/(1 - x^2)^(3/2)$

1015 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-10-01T14:50:34

The answer is $=x/sqrt(1-x^2)+C$

We need $intsec^2x dx=tanx$

We perform this integral by substitution

Let $x=sintheta$ , $=>$ , $dx=costheta d theta$

$1-x^2=1-sin^2theta=cos^2theta$

$tan theta=sintheta/cos theta=x/sqrt(1-x^2)$

Therefore,

$int(dx)/(1-x^2)^(3/2)=int(costhetad theta)/(cos^2)^(3/2)$

$=int(d theta)/(cos^2theta)$

$=intsec^2theta d theta$

$=tantheta$

$=x/sqrt(1-x^2)+C$