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Integration by tables

  1. Feb 16, 2014 #1
    1. The problem statement, all variables and given/known data
    Integrate sin^-1(sqrtx)

    2. Relevant equations

    3. The attempt at a solution
    To solve this, I first made a substitution of u=arcsin(sqrtx) so dx=sqrt(1-u)du

    Still pretty difficult to solve, so I integrated by parts with v=sqrt(1-u) dw=udu dv=(1/2)(sqrt(1-u))2 and w=(1/2)(u^2)
    To integrate this new equation, I used a table to get this: sqrt(1-u)(1/2)(u^2) + (1/2)arcsinu + c

    I put this all together and changed the u to arcsin(sqrtx).

    I'm wondering if this was a legit way of solving this equation.
  2. jcsd
  3. Feb 16, 2014 #2
    You misused the Chain Rule here.
  4. Feb 17, 2014 #3
    You're right, I just saw that that will leave me with root 1-x du not 1-u, thanks
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