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?

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- Feb 26th 2009, 05:09 AMMathsnewbieIntegration
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? - Feb 26th 2009, 05:26 AMKrizalid
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 $\displaystyle x=\tan\varphi.$ - Feb 26th 2009, 06:07 AMMathsnewbie
Can you explain to me how the tan part works please?

- Feb 26th 2009, 06:48 AMHallsofIvy
It x= tan(t), then $\displaystyle 1+ t^2= 1+ tan^2(t)= sec^2(t)$ so that $\displaystyle \sqrt{1+ t^2}= sec(t)$ and $\displaystyle du= sec^2(t)dt$.