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Integral of (x^2)(sqrt(x^3 + 1))dx. Please check my work? Thank you!

  1. Jan 18, 2013 #1
    ∫x^2(√(x^3 + 1))


    u = x^3 + 1
    du = 3x^2dx
    (1/3)du = x^2dx

    ∫√(u)*(1/3)du

    = 2/3(u)^3/2 *(1/3)

    = 2/9(x^3 + 1)^3/2

    Is this the correct answer? Thank you.
     
  2. jcsd
  3. Jan 18, 2013 #2
    Yep, looks like it. You can always differentiate your answer if you're not sure.
     
  4. Jan 18, 2013 #3

    Mentallic

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    Yes, but don't forget about the constant of integration.
     
  5. Jan 20, 2013 #4
    Thanks, you guys! :)

    That's true. I should differentiate when I'm not sure...
     
  6. Jan 20, 2013 #5

    Ray Vickson

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    You should differentiate even when you are sure! (Sometimes a person can be sure but still have the wrong answer.)

    In other words: always differentiate!
     
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