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Help with integral

  1. Jun 10, 2015 #1
    1. The problem statement, all variables and given/known data
    The problem is this:
    ∫[√x /(1+x)] dx
    I used sustitution method
    u= √x
    u^2=x
    2udu=dx


    2. Relevant equations
    My new integral is:
    ∫[(u*2udu)/(1+u^2)]du
    2∫[u^2/(1+u^2)]du
    I need help to reduce this point to continue, I guess I need some algebraic steps

    3. The attempt at a solution

    The book shows: x^3/3 -3x - 10Ln|x-5| + C as the answer but I think this is wrong because I don't have x-5 anywhere
     
  2. jcsd
  3. Jun 10, 2015 #2

    Mark44

    Staff: Mentor

    This looks OK. I would use polynomial long division to turn this improper rational expression into a nicer form for integration. If you're not familiar with this technique, do a web search for "polynomial long division".
    I agree - the book's answer doesn't look right.
     
  4. Jun 10, 2015 #3

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Hello ArmandStarks. Welcome to PF !

    You can use "long division" to divide u2 by (u2 + 1) .

    Or use the following "trick" .

    ##\displaystyle \frac{u^2}{1+u^2}=\frac{u^2+1-1}{1+u^2}##

    ##\displaystyle =\frac{1+u^2}{1+u^2}-\frac{1}{1+u^2}##​
     
  5. Jun 10, 2015 #4
    I just found that "trick" and the 2 integrals are easy to do.
    Thank you both!
     
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