Trig Derivative

1. Oct 26, 2004

tangur

$$\int \frac {x^2}{\sqrt{4x-x^2}}dx$$

I just want to be sure I'm right on this, complete the square first of all so you get $$-\int \frac {x^2}{\sqrt{(x-2)^2-4}}dx$$ let $$u=x-2$$ thus $$-\int \frac {(x+2)^2}{\sqrt{u^2-4}}dx$$then let$$u=2sec(\theta)$$
hence integral becomes $$-8\int sec^3(\theta)+2sec^2(\theta)+sec(\theta)d\theta$$

and then solve.

Thanks

Last edited: Oct 26, 2004
2. Oct 26, 2004

Parth Dave

I got -4 as the constant

3. Oct 26, 2004

ReyChiquito

the first integral is always positive, the second one doesnt. You cant just invert the sign on the radical and take one minus out... the sign on the radical should stay, wich, if you think about it, might make things easier

4. Oct 27, 2004

tangur

true, since its under a sqrt root, you keep it under, but you put the whole expression under square root in parenthesis and take out the minus one, and then go x^2-4x. makes sense

thx guys