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Calculus Substitution Rule Problem Check

  1. Nov 30, 2008 #1
    1. The problem statement, all variables and given/known data

    Evaluate the indefinite integral...

    [itex]\int x^2 (x^3+5)^9 dx[/itex]

    2. Relevant equations

    [itex]\int f(g(x))g'(x)dx = \int f(u)du[/itex]

    3. The attempt at a solution

    [itex]u = x^3+5[/itex]

    [itex]du = x^2dx[/itex]

    So my answer is...

    [​IMG]

    Does that look right?

    And one more...

    1. The problem statement, all variables and given/known data

    Evaluate the indefinite integral...

    [itex]\int x/(x^2+1)^2[/itex]

    2. Relevant equations

    [itex]\int f(g(x))g'(x)dx = \int f(u)du[/itex]

    3. The attempt at a solution

    [itex]u = x^2+1[/itex]

    [itex]du = 1/2 dx[/itex]

    So my answer is...

    [itex](-1)/2(x^2+1) + C[/itex]

    Does that look right?
     
    Last edited: Nov 30, 2008
  2. jcsd
  3. Nov 30, 2008 #2
    Since you are solving indefinite integrals, to check your answer simply differentiate and see if it is same as the function under the integral.
     
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