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Math Help - Integration by Substitution

  1. #1
    Senior Member topher0805's Avatar
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    Integration by Substitution

    My teacher wants me to solve this by substitution:

    \int^7_0 \frac{x}{\sqrt{1+5x}}

    My work so far:

    u = 1+5x

    du = 5

    x = \frac{u-1}{5}

    dx = \frac{1}{5}

    Not sure where to go from here...
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  2. #2
    MHF Contributor
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    Quote Originally Posted by topher0805 View Post
    My teacher wants me to solve this by substitution:

    \int^7_0 \frac{x}{\sqrt{1+5x}}

    My work so far:

    u = 1+5x

    du = 5

    x = \frac{u-1}{5}

    dx = \frac{1}{5} \,du don't forget this du

    Not sure where to go from here...
    Switch your limits x = 0, u = 1,\;\;\;x = 7, u = 36and put in the pieces

    \frac{1}{25}\, \int_1^{36} \frac{u-1}{\sqrt{u}}\, du

    now expand and integrate.
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