Splitting Fractions (Integrals)

[FuturEngineer]

Homework Statement

Evaluate

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

Homework Equations

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

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! [/B]

 

[deedsy]

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

 

[Mark44]

Homework Statement

Evaluate

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

Homework Equations

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

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! [/B]

Looks like a natural for trig substitutions for both integrals

 

[HallsofIvy]

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

 

[Mark44]

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

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

 

[FuturEngineer]

Thanks!