Expert: Paul Klarreich - 6/23/2010

Question
Evaluate the integral of dx/(x^2 + 1)^2 from 0 to 1 by making the substitution x = tanu; remember the limits.

Answer
Questioner: Krystal
Country: United States
Category: Calculus
Private: No
Subject: Help ASAP Please
Question: Evaluate the integral of dx/(x^2 + 1)^2 from 0 to 1 by making the substitution x = tanu; remember the limits.
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If x = tan u, then dx = sec^2 u,  x^1 + 1 = sec^2 u,  (x^2 + 1)^2 = sec^4 u

Then you will have  cos^2 u to integrate.  Use the half-angle trick.

That should do it nicely.  At the end, you will make u = arctan x before you apply the limits.

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