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Math Help - Definite integral

  1. #1
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    Definite integral

    help with finding the definite integral using u substitution.
    ({sec^2[1/x^37]}/x)dx. U=(1/x^37)

    And

    x^3(2 + x^4)^6 dx. U =(2 + x^4).
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  2. #2
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    Quote Originally Posted by doneng View Post

    x^3(2 + x^4)^6 dx. U =(2 + x^4).
    Your first one does not make sense so I do this one.
    If u=2+x^4 then (2+x^4)^6 = u^6 and u'=4x^3.

    Thus we will write, \int (2+x^4)^6x^3 dx = \frac{1}{4}\int \underbrace{(2x+x^4)^6}_{u^6}\underbrace{[4x^3]}_{u'} dx = \frac{1}{4}\int u^6 du

    This integral is, \frac{1}{28}u^7 + C = \frac{1}{24}(2+x^4)^7 + C.
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