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Homework Help: Integration of a complicated radical function

  1. Dec 4, 2013 #1
    1. The problem statement, all variables and given/known data

    ∫(√x).[√(x+1)] dx

    2. Relevant equations

    3. The attempt at a solution

    Sorry but i couldn't get it any far than this u substitution

    u = √(x+1)
    du = [(1)/{2√(x+1)}]dx

    → dx = [2√(x+1)]du

    putting in the main expression

    ∫ √(u2 - 1). 2u2 du
  2. jcsd
  3. Dec 4, 2013 #2


    Staff: Mentor

    Here's a different approach. Combine the two radicals like so:
    ##\int \sqrt{x}\sqrt{x + 1}dx = \int \sqrt{x^2 + x}dx##

    Now, complete the square inside the radical to get √[(x + a)2 - b2]. At this point a trig substitution should work, assuming you have learned that technique.
  4. Dec 4, 2013 #3
    so that was mathematically valid : O to multiply..poor algebra me :(
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