Posted by **Jay** on Thursday, May 24, 2012 at 10:29pm.

Trying to find ∫x*arctan(x)dx, but I can't figure out what do to after:

(1/2)x^2*arctan(x)-1/2∫x^2/(x^2+1) dx

- Integral Calculus -
**Bosnian**, Thursday, May 24, 2012 at 10:41pm
In google type:

wolfram alpha

When you see list of results click on:

Wolfram Alpha:Computational Knowledge Engine

When page be open in rectangle type:

integrate x*arctan(x)dx

and click option =

After few secons you will see result.

Then click option : Show steps

- Integral Calculus -
**Jay**, Thursday, May 24, 2012 at 10:45pm
great, I can find the steps and i have the answer already. i just don't understand the step to be made after (1/2)x^2*arctan(x)-1/2∫x^2/(x^2+1) dx

- Integral Calculus -
**Ethan**, Thursday, May 24, 2012 at 10:51pm
To solve that last integral, you have to use the substitution rule.

u= x^2 + 1

du= 2x

Therefore the integral becomes:

-1/2∫(2/u) du

Factor out the 2

-∫1/u du

Integrate

-ln(u)

Which is equal to

-ln(x^2 +1)

Since u= x^2 + 1

- Integral Calculus -
**Jay**, Friday, May 25, 2012 at 2:35am
I figured it out

@Ethan, you can't substitute because it is x^2 over(x^2+1)

- Integral Calculus -
**MathMate**, Friday, May 25, 2012 at 9:50am
x^2/(x^2+1) = 1 - 1/(x^2+1)

You can easily integrate that.

- Integral Calculus -
**Ethan**, Friday, May 25, 2012 at 10:50am
Sorry, I misread that as 2x instead of x^2.

- Integral Calculus :) -
**MathMate**, Friday, May 25, 2012 at 11:35am
No problem!

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