Can This Integral Be Solved Using Factoring and Substitution?

[whatlifeforme]

Homework Statement

evaluate the integral.

Homework Equations

$\displaystyle\int {\frac{3x+2}{\sqrt{1-x^2}} dx}$

The Attempt at a Solution

- i tried factoring hoping for a perfect square that i could take the square root of, but that doesn't work.

-u-sub won't work: u=1-$x^2$ ; du=2x

-i don't know how to use that denominator in partial fractions.

 

[Curious3141]

Homework Statement

evaluate the integral.

Homework Equations

$\displaystyle\int {\frac{3x+2}{\sqrt{1-x^2}} dx}$

The Attempt at a Solution

- i tried factoring hoping for a perfect square that i could take the square root of, but that doesn't work.

-u-sub won't work: u=1-$x^2$ ; du=2x

Break it up into two:$\int\frac{3x}{\sqrt{1-x^2}}dx + \int\frac{2}{\sqrt{1-x^2}}dx$.

Observe that $3x = -\frac{3}{2}*(-2x)$, and now you should be able to make an obvious sub to resolve the first integral.

For the second integral, just make a simple trig sub.

Partial fractions wouldn't work here because of that square root in the denominator.