# Thread: struggling with integration

1. ## struggling with integration

Hi can someone please help me with this and explain how you get the answer.

find the integral of X/(sqrtX^2+4) dx

any help would be much appreciated.
Thanks

2. ## Re: struggling with integration

I assume you are given:

$\int\frac{x}{\sqrt{x^2+4}}\,dx$

What do you think is a good candidate for a u-substitution?

3. ## Re: struggling with integration

yeah am not really sure where to start with this one.

i thought that u=sqrtx^2+4 which makes it x+4 correct?

4. ## Re: struggling with integration

Isn't the entire expression $x^2+4$ under the radical?

If so, then try:

$u=x^2+4\:\therefore\:du=2x\,dx$

Is there a way for us to manipulate the integral so that we have a $2x\,dx$ inside the integral?

5. ## Re: struggling with integration

im sure there is but i cant figure it out at the min. must have missed the part of class where they explained this

6. ## Re: struggling with integration

Multiply by 2 inside and by 1/2 in front, for a net result of multiplying by 1. So that you have:

$\frac{1}{2}\int\frac{2x}{\sqrt{x^2+4}}\,dx$

Now, using the aforementioned substitution, how may we write this?

7. ## Re: struggling with integration

think i have it 1/2 int 1/sqrt U du

so answer once you substitute back is sqrt(X^2+4.)+C

8. ## Re: struggling with integration

Yes, that is correct.

9. ## Re: struggling with integration

thank you for your help and patience !!!

10. ## Re: struggling with integration

Glad to help and glad you stuck it out!