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Math Help - integrating

  1. #1
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    integrating

    hello,
    can anyone please help intergrate this, i dont know how to do square root integration...

     <br />
\int{x^5\sqrt{x^6+7}dx}<br />
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  2. #2
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by drewbear View Post
    hello,
    can anyone please help intergrate this, i dont know how to do square root integration...

     <br />
\int{x^5\sqrt{x^6+7}dx}<br />
    use substitution:

     u = {x^6}+7 \rightarrow du = 6x^5 dx \rightarrow dx = \frac{du}{6x^5}

    put the above in your integration:

    \int {x^5\sqrt{x^6+7}dx}

    = \int{x^5\sqrt{u}} \frac{du}{6x^5}

    = \int \frac{\sqrt{u}}{6}   du

    solve
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  3. #3
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    <br />
u = {x^6}+7 \rightarrow du = 6x^5 dx \rightarrow dx = \frac{du}{6x^5}
    the part here where you solve for dx from du we havent been taught yet, but going along with the substitution you said i got to:

     <br />
\frac{1}{6}\int{\sqrt{u}}<br />

    but what would the integration of that be??
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  4. #4
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by drewbear View Post
    the part here where you solve for dx from du we havent been taught yet, but going along with the substitution you said i got to:

     <br />
\frac{1}{6}\int{\sqrt{u}}<br />

    but what would the integration of that be??
     <br />
\frac{1}{6}\int{\sqrt{u}}<br />

    = \frac{1}{6}\int u^{\frac{1}{2}} du

    = \frac{1}{6} \times [ \frac{2}{3} \times {u^{\frac{3}{2}}}] + C

    Now substitute the value of u = {x^6}+7 in the above equation
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