Splitting Fractions (Integrals)

1. Apr 10, 2015

FuturEngineer

1. The problem statement, all variables and given/known data
Evaluate

Integrate (2-3x/(Sqrt.(1 - x^2))) dx

2. Relevant equations
1/Sqrt.(1-x^2) = arctan

3. The attempt at a solution
I am so lost, but this is what I've tried, but didn't work...

I separated the integral into two so
Integral of (2/(Sqrt.(1-x^20))) dx - integral of (3x/(Sqrt.(1-x^2))) dx
I am not sure how to proceed? Help!

2. Apr 10, 2015

deedsy

this can be solved using a trig substitution for x. Can you think of what this substitution should be to simplify the denominator?

3. Apr 10, 2015

Staff: Mentor

Looks like a natural for trig substitutions for both integrals

4. Apr 10, 2015

HallsofIvy

Staff Emeritus
I would NOT use a trig substitution for $\frac{3x}{\sqrt{1- x^2}}$. Instead let $u= 1- x^2$

5. Apr 10, 2015

Staff: Mentor

A trig substitution would work, but I agree that an ordinary substitution (as you suggest) would be easier, which makes it a better choice.

6. Apr 10, 2015

Thanks!