integration problem

[Mr. Ne Ed help]

How do you integrate this problem?

int (x tan^(-1) x dx)

I have no idea how to get started.

Thanks.

 

[Matt]

Integration by parts. Integrate x and differentiate tan^(-1)x.

 

[soroban]

Hello, Mr. Ne Ed help!

Matt is absolutely correct . . .

∫ x tan^-1(x) dx.

Let: u = tan^-1(x) . . . . . dv = x dx

. . . . . . . . . . . dx
Then: du = -------- . . . v = (1/2)x²
. . . . . . . . . 1 + x²

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .x²
And we have: . (1/2)x²tan^-1(x) - (1/2) ∫ --------- dx
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1 + x²

Can you finish it now?

 

[Mr. Ne Ed help]

Yes, I can finish it now. Thank you everyone.