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Math Help - Integral Method using the Substitution Method

  1. #1
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    Integral Method using the Substitution Method

    Hey There,
    I am doing a question and I can solve it the antiderivative way, but I can't seem to come up with the substitution method.
    3 + x^3/2 dx
    __ _____ divide by
    x^3 3

    So I put the integral sign 3x^-3 - 3x^3/2 dx
    now do I take out a 3 and have 3(x^-3-3x^3/2) dx or NO??

    I can't figure out the U and du.

    Any help would be great, thanks.
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  2. #2
    Ted
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    Re: Integral Method using the Substitution Method

    this is your integral ?

    \displaystyle \int \dfrac{3 + \dfrac{x^3}{2} }{ 3 x^3} \, dx
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  3. #3
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    Re: Integral Method using the Substitution Method

    Hello, bradycat!

    \int \left(\frac{3}{x^3} + \frac{x^{\frac{3}{2}}}{3}\right)\,dx

    We have: . \int\left(3x^{-3} + \tfrac{1}{3}x^{\frac{3}{2}}\right)\,dx

    . . . . . . =\;\frac{3x^{-2}}{-2} + \frac{\frac{1}{3}x^{\frac{5}{2}}}{\frac{5}{2}} + C

    . . . . . . =\;-\frac{3}{2x^2} + \frac{2}{15}x^{\frac{5}{2}} + C

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