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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