Can anyone help me find the intergral of this, need to know how for my workshop in a couple of hours.
X+1/(1+x^2)^3/2 dx
I tried substitution but didn't get far, any help?
This is $\displaystyle \int{\frac{x}{\left( 1+x^{2} \right)^{3/2}}\,dx}+\int{\frac{dx}{\left( 1+x^{2} \right)^{3/2}}}.$
The first integral is easy, just put $\displaystyle u^2=1+x^2.$ As for the second one, you can perform the standard trigonometric substitution $\displaystyle x=\tan\varphi.$