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Thread: Integration using U sub

  1. #1
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    Integration using U sub



    I know its U substitution with u= 4+3s^2 and du=6xdx but I dont know how to make 13 s drop out?
    Thanks to anyone who can help
    Amanda
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  2. #2
    Member Black's Avatar
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    $\displaystyle du=6s \, ds \Longrightarrow \frac{13}{6}du=13s \, ds.$
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  3. #3
    Newbie Homeomorphism's Avatar
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    Quote Originally Posted by Casas4 View Post
    I know its U substitution with u= 4+3s^2 and du=6xdx ...
    Which means $\displaystyle dx = \dfrac{du}{6x}$. Substituting $\displaystyle \dfrac{du}{6x}$ for $\displaystyle dx$ and $\displaystyle u$ for $\displaystyle 4+3s^2$ gives: $\displaystyle \int\left(\dfrac{13s}{u}\right)\left(\dfrac{du}{6s }\right)\;{du} = \int\left(\dfrac{13s}{6s}\right)\left(\dfrac{1}{u} \right)\;{du}$. The $\displaystyle s$ in the numerator and the $\displaystyle s$ in the denominator cancel, so it becomes: $\displaystyle \frac{13}{6}\int\frac{1}{u}du$.
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