Using U-Substitution to Find an Integral

[lch7]

So I was messing around with some basic u-sub calculus and came across this problem. Any help would be greatly appreciated!

Homework Statement

\int \frac{3x^{2}}{x^{2}-7} dx

Homework Equations

I'm using u-substitution, as stated at the beginning.

The Attempt at a Solution

I see that the u could be the denominator and the numerator is the derivative, or du.

\int \frac{du}{u}

\int \frac{1}{u} du

ln|u|+C

ln|x^{2}|+C

I'm pretty sure this is the correct answer, but I decided to integrate it with the boundaries x=1 and x=4.5.

[ln|x^{2}-7|]^{4.5}_{1}

ln|13.25| - ln|-6|
ln(13.25) - ln(6)
2.5839-1.7917
.7922

So this is my final answer, but it just doesn't seem right. I graphed the function and saw it was under the x-axis. Is this the problem?

 

[LCKurtz]

So I was messing around with some basic u-sub calculus and came across this problem. Any help would be greatly appreciated!

Homework Statement

\int \frac{3x^{2}}{x^{2}-7} dx

Homework Equations

I'm using u-substitution, as stated at the beginning.

The Attempt at a Solution

I see that the u could be the denominator and the numerator is the derivative, or du.

But if $u=x^2-7$ then $du = 2xdx$ and that is not what you have in the numerator. Try one long division step and see what to do next.

 

[STEMucator]

Following what Lc suggested, here's a hint that will make it easier : $x^2 - 7 = (x + \sqrt{7})(x - \sqrt{7})$.

 

[lch7]

Oh man I feel like an idiot! Thankyou all!