# Using U-Substitution to Find an Integral

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?

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

Oh man I feel like an idiot!! Thankyou all!