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Homework Help: Integrate 3t^2(1+t^3)^4

  1. Jun 21, 2007 #1
    1. The problem statement, all variables and given/known data
    Integrate the following:
    \int {3t^2 \left( {1 + t^3 } \right)^4 \,\,dt}

    2. Relevant equations
    \int {\left( {a + bx} \right)^n \,\,dx = \frac{{\left( {a + bx} \right)^{n + 1} }}{{a\left( {n + 1} \right)}} + c} \\
    \int {x^n \,\,dx = \frac{{x^{n + 1} }}{{n + 1}} + c} \\

    3. The attempt at a solution
    I am unsure on how to integrate problems such as these. Is there another rule? or is it a combination of rules? Many thanks to all help provided,
  2. jcsd
  3. Jun 21, 2007 #2


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    One way would be to integrate by parts a few times. There's probably a quicker way that someone else may spot though.
  4. Jun 21, 2007 #3
    how would i integrate by parts in there situations? thanks\
  5. Jun 21, 2007 #4
    No need for integration by parts. Look at the "1 + t^3" term. What is it's derivitive. This problem can be solve by a simple substitution. Do you see it?
  6. Jun 21, 2007 #5


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    Haha, nice.. I knew there would be a quicker way!
  7. Jun 22, 2007 #6
    okay i can solve the problem now, thanks all
  8. Jun 22, 2007 #7

    Gib Z

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    Homework Helper

    Longer than a substitution, but shorter than integration by parts a few times, would be the expansion of the factorized expression and integrate term by term.
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