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

Question

(1/2)x^2*arctan(x)-1/2∫x^2/(x^2+1) dx

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

x^2/(x^2+1) = 1 - 1/(x^2+1)
You can easily integrate that.

Answer 6

Sorry, I misread that as 2x instead of x^2.

Answer 7

No problem!