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Indefinite integral

  1. Dec 6, 2007 #1
    1. [tex]\int[/tex](x[tex]^{2} + 5)^{3}dx[/tex]

    This is what the book gives as the answer
    1/7x[tex]^{7}[/tex] + 3x[tex]^{5}[/tex] + 25x[tex]^{3}[/tex] + 125x + C

    I got something way different. Where are they getting the 3x^5 and 25x^3 from? Thanks.

    -v.b.
     
  2. jcsd
  3. Dec 6, 2007 #2
    What was your result?
     
  4. Dec 6, 2007 #3
    Oh, I got: 1/7x^7 + 125x but I distributed the power and started off with x^6 + 125 before anti deriving.
     
  5. Dec 6, 2007 #4
    That would be the problem. You didn't distribute the power correctly. What you did was

    [tex](x^2 + 5)^3 = (x^2)^3 + 5^3[/tex]​

    But that's not true. The correct way to expand the power is

    [tex](x^2 + 5)(x^2 + 5)(x^2 + 5)[/tex]​

    So, for example

    [tex](x+1)^2 = (x+1)(x+1) = x*x + 1*x + 1*x + 1*1 = x^2 + 2x + 1[/tex]​

    Not

    [tex](x+1)^2 = x^2 + 1^2[/tex]​
     
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