Math Help - Integration

1. Integration

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?

2. This is $\int{\frac{x}{\left( 1+x^{2} \right)^{3/2}}\,dx}+\int{\frac{dx}{\left( 1+x^{2} \right)^{3/2}}}.$

The first integral is easy, just put $u^2=1+x^2.$ As for the second one, you can perform the standard trigonometric substitution $x=\tan\varphi.$

3. Can you explain to me how the tan part works please?

4. It x= tan(t), then $1+ t^2= 1+ tan^2(t)= sec^2(t)$ so that $\sqrt{1+ t^2}= sec(t)$ and $du= sec^2(t)dt$.