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
Isn't the entire expression $\displaystyle x^2+4$ under the radical?
If so, then try:
$\displaystyle u=x^2+4\:\therefore\:du=2x\,dx$
Is there a way for us to manipulate the integral so that we have a $\displaystyle 2x\,dx$ inside the integral?
Multiply by 2 inside and by 1/2 in front, for a net result of multiplying by 1. So that you have:
$\displaystyle \frac{1}{2}\int\frac{2x}{\sqrt{x^2+4}}\,dx$
Now, using the aforementioned substitution, how may we write this?