The Substitution Method

[roam]

Evaluate the following integral using integration by substitution: http://img254.imageshack.us/img254/750/44900023cm4.png [Broken][/URL]




Here is my attempt:
Let x = sinu, then dx/du = cosu
Substituting gives, ∫1/(1-sin2u)×cosu du
= ∫1/(1-sin2u)×cosu du
= ∫cosu/√cos2u du
= ∫cosu/cosu du
= ∫1 du = u + c = sin-1x + c

Am I right? Did I get the right solution?

Regards,

 

[rocomath]

You don't need Trig sub. for this.

$$\int\frac{xdx}{\sqrt{1-x^2}}$$

But we'll go with it!

$$x=\sin u$$
$$dx=\cos udu$$

$$\int\frac{\sin u \cos u du}{\sqrt{1-\sin^2 u}}$$

 

[Feldoh]

Try u=1-x^2 instead... Might be a bit easier.