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Homework Help: Help! I'm in college and have forgotten everything!

  1. Sep 15, 2006 #1
    Hi. I am in college and have forgotten everything about how to solve indefinite integrals.

    Even very simple problems give me trouble, such as:

    int( y^3 * sqrt(2y^4 - 1) ) dy

    So how in the world do you find the answer? The Antiderivative? Please go through this step-by-step, I need a good jumpstart to get myself in the right frame of mind again.
  2. jcsd
  3. Sep 15, 2006 #2
    So you have [tex] \int y^{3}\sqrt{2y^{4}-1} dy [/tex]. Let [tex] u = 2y^{4} -1 [/tex], then [tex] du = 8y^{3} dy [/tex]. But there is only a [tex] y^{3} dy [/tex] available so we have to multiply the integral by [tex]\frac{1}{8} [/tex]:

    [tex] \frac{1}{8} \int u^{\frac{1}{2}} du = \frac{1}{12}(2y^{4}-1)^\frac{3}{2} + C [/tex]
    Last edited: Sep 15, 2006
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