1. ## Integration

Find the following integrals:

a) integral from -1 to 0 of 1/(sqrt of 1-x) dx
b) indefinite integral of x(ln(x))^2 dx
c) indefinite integral of (x+7)/((x-3)(x+2)) dx

My final exam is almost here. I need help!
This is a practice question and for part a, I got -2+2sqrt2
Part b: (ln(x))^2 * x^2/2 - lnx * x^2/2 - x^2/4 + C
Part C: ln of absolute value of (x-3)^2/(x+2) +C

2. Originally Posted by Mathbo
Find the following integrals:

a) integral from -1 to 0 of 1/(sqrt of 1-x) dx
b) indefinite integral of x(ln(x))^2 dx
c) indefinite integral of (x+7)/((x-3)(x+2)) dx

My final exam is almost here. I need help!
This is a practice question and for part a, I got -2+2sqrt2
Part b: (ln(x))^2 * x^2/2 - lnx * x^2/2 - x^2/4 + C
Part C: ln of absolute value of (x-3)^2/(x+2) +C
Yes all fine.

Yes all fine.
Seriously?
What method am I supposed to use for part C?

4. Originally Posted by Mathbo
Seriously?
What method am I supposed to use for part C?
In your post you said you solved it so whatever method you used is fine. Probably partial fractions or something like that. It's 3am so I can't give it tooo much thought...

In your post you said you solved it so whatever method you used is fine. Probably partial fractions or something like that. It's 3am so I can't give it tooo much thought...
Did you do the actual integration and actually get the same answers as I did? I'm worried that I have problems with integration. And my final is tomorrow!
Thanks!

6. Originally Posted by Mathbo
Did you do the actual integration and actually get the same answers as I did? I'm worried that I have problems with integration. And my final is tomorrow!
Thanks!
use partial fractions to get:

$\displaystyle \int \frac{x+7}{x-3)(x+2)} dx = \int [\frac{2}{x-3} -\frac{1}{x+2}] dx$

and integrate

7. Well i too solve it. Your answer is right. But the calculations to shown on the post is so difficult so i suggest you to just be relax that you are right in your calculation. Also i would suggest you to don't delete this post because it could be helpful you to ask and take solutions in your any other difficulties.

8. Originally Posted by Mathbo
Did you do the actual integration and actually get the same answers as I did? I'm worried that I have problems with integration. And my final is tomorrow!
Thanks!
I did it with Maple. I'd say you'll be fine.

9. By partial integration

∫{(x+7)/(x-3)(x+2)}dx=∫{A/(x-3)+B/(x+2)}dx

A(x+2)+B(x-3)=x+7

Let x=3

5A=10

A=10/5
A=2

Let x=-2

-5B=5

B=-1

∫{(x+7)/(x-3)(x+2)}dx=∫{2/(x-3)-1/(x+2)}dx

=∫{2/(x-3)dx- ∫1/(x+2)}dx

=2ln(|x-3|)-ln(|x+2|)+C