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Arctan integration question

  • Thread starter Pyroadept
  • Start date
  • #1
89
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Homework Statement


∫xarctanx dx


Homework Equations


d/dx (arctanx) = 1/(1 + x^2)
∫1/(1 + x^2) = arctanx
∫u dv = uv - ∫v du

The Attempt at a Solution


Hi everyone,

Here's what I've done so far:

Use integration by parts:
u = arctanx
du = 1/(1 + x^2) dx

dv = x dx
v = (1/2)x^2

∫u dv = uv - ∫v du
= arctanx(1/2)x^2 - (1/2)∫x^2/(1 + x^2) dx

But how do you integrate this new integral without going back into arctanx, in which case you'll be left with zero?

Thanks for any help
 

Answers and Replies

  • #2
benorin
Homework Helper
1,100
14
Long division. [tex]\frac{x^2}{1+x^2}=1-\frac{1}{1+x^2}[/tex]
 

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