# struggling with integration

• Sep 9th 2012, 11:54 PM
rich1979
struggling with integration

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

any help would be much appreciated.
Thanks
• Sep 9th 2012, 11:58 PM
MarkFL
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?
• Sep 10th 2012, 12:15 AM
rich1979
Re: struggling with integration

i thought that u=sqrtx^2+4 which makes it x+4 correct?
• Sep 10th 2012, 12:27 AM
MarkFL
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?
• Sep 10th 2012, 01:15 AM
rich1979
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
• Sep 10th 2012, 01:20 AM
MarkFL
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?
• Sep 10th 2012, 01:45 AM
rich1979
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
• Sep 10th 2012, 02:02 AM
MarkFL
Re: struggling with integration
Yes, that is correct. :)
• Sep 10th 2012, 02:13 AM
rich1979
Re: struggling with integration
thank you for your help and patience !!!
• Sep 10th 2012, 02:16 AM
MarkFL
Re: struggling with integration