How Do You Integrate x/(sqrt[1+x^2])?

[Brewer]

I have to integrate:
x/(sqrt[1+x^2]) dx

I know the answer is sqrt[1+x^2], but I can't work out how to get there. I tried the substitution u = 1+x^2, but that didn't seem to get me any where. It also looks like the differential of arsinx, but its not quite. How do I get to the answer?

Any help would be greatly appreciated.

Thank you in advance

 

[matt grime]

Why didn't that subs help: it transforms it up to a scalar multiple to the integral of u^{-1/2}, which you know how to do.

 

[Brewer]

i managed to confuse myself, when getting du.

if u = 1 + x^2

then du/dx = 2x

so du = 2x dx yes?

so does that mean that the integral is now 0.5u^(-1/2)?

I can't remember what to do when I get to that stage.

Thanks though

 

[TensorKhan]

i managed to confuse myself, when getting du.

if u = 1 + x^2

then du/dx = 2x

so du = 2x dx yes?

so does that mean that the integral is now 0.5u^(-1/2)?

I can't remember what to do when I get to that stage.

Thanks though

From what I can see, that is correct. Now simply integrate through:

$$\int\frac{du}{2\sqrt{u}}$$

and follow through with your answer.

 

[Brewer]

Ta. It makes more sense now.

Thankyou, both of you