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Math Help - simple integration problem

  1. #1
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    simple integration problem

    I'm trying to review some simple integration to help me with an upcoming test. i'm stuck on this one. i need to know how to solve it with substitution.


    \int{(x^3)(\sqrt{x^2+1})dx}
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  2. #2
    MHF Contributor matheagle's Avatar
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    Let u=x^2+1 thus du=2xdx

    and rewrite your integral as \int x^2 x\sqrt{x^2+1}dx

    = {1\over 2} \int x^2 \sqrt{x^2+1}(2xdx)

    ={1\over 2}\int (u-1)\sqrt{u} du

    ={1\over 2}\int (u^{3/2}-u^{1/2}) du

    Now you can integrate and replace the u's with the x's.
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  3. #3
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    thankyou very much
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