Posted by Jay on .
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,
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,
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,
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,
I figured it out
@Ethan, you can't substitute because it is x^2 over(x^2+1) 
Integral Calculus 
MathMate,
x^2/(x^2+1) = 1  1/(x^2+1)
You can easily integrate that. 
Integral Calculus 
Ethan,
Sorry, I misread that as 2x instead of x^2.

Integral Calculus :) 
MathMate,
No problem!