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Integration by parts

  1. Jun 2, 2016 #1
    1. The problem statement, all variables and given/known data

    upload_2016-6-2_21-5-50.png

    2. Relevant equations
    ∫ f(x) g'(x) dx = f(x) g(x) - ∫ f '(x) g(x) dx

    f(x)=√(1+x^2)
    f '(x)=x * 1/√(1+x^2)

    g'(x)=1
    g(x)=x

    3. The attempt at a solution
    ∫ √(1+x^2) * 1 dx
    =x * √(1+x^2) - ∫ x^2 * 1/√(1+x^2) dx

    Further integration just makes the result look further from what it's supposed to look like
     
  2. jcsd
  3. Jun 2, 2016 #2
    The latter part may help to go to your answer. You maybe can try to make it become ##\frac{x^2}{\sqrt{1+x^2}}=\sqrt{1+x^2}-\frac{1}{\sqrt{1+x^2}}.##
     
  4. Jun 2, 2016 #3
    Thank you!
     
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