# A couple of Integration problems

1. Oct 19, 2009

### star001

A couple of Integration problems 9dx/(x(x^4 + 8 ))

1. The problem statement, all variables and given/known data

Hi

I'm new to this forum. I have a couple of Integration Problems which im not able to integrate correctly. I will also post my attempt at solving the problem so u guys can see what method i took trying to solve these. spent a lot of time in these questions and finally decided to post in this forum.

1
9dx/(x(x^4 + 8 ))

2
integ 37dx/((root(x)+ xroot(x))

3. The attempt at a solution

My attempt

i tried u substitution with u=x^2
also 9 is a constant so i took it out for the time being(ill multiply the answer i get with 9)

9 integ dx/(x(x^4 + 8 )) u = x^2 du=2xdx
9 integ xdx/(x^2(x^4 + 8 ))
9*1/2 integ du/(u(u^2 + 8 )

9*1/2 integ du/(u^3 + 8u ) ??
9*1/2 (ln|u^3 +8u|) <<is that answer correct?

if not can someone kindly tell me how to do this problem pls.

I do not know how to go about the 2nd problem. any hints on how to approach it are welcome :)

Last edited: Oct 19, 2009
2. Oct 19, 2009

### Donaldos

1. Decompose $$\frac{1}{x\left(x^4+8\right)}$$ into partial fractions

2. $$u=\sqrt{x}$$ + partial fraction decomposition

3. Oct 19, 2009

### Staff: Mentor

Re: A couple of Integration problems 9dx/(x(x^4 + 8 ))

So far so good, but the next line is not correct.
$$\int \frac{du}{u}~=~ln|u| + C$$
but you don't have just exactly u in the denominator; you have u3 + 8u. To work through that integral you probably need a technique called partial fraction decomposition, AKA partial fractions.
For your second problem, I would start with a substitution u = sqrt(x), and see where that takes you.

4. Oct 20, 2009

### star001

Thanks a lot guys!