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Math Help - Integration by substitution

  1. #1
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    Integration by substitution

    Hi there. I'm new here :-)

    I've been going through a fair few substitution questions, but I have been stumped on this one.

    I have to solve the following by substitution:
    <br />
\int \sqrt{x^3+1} *  x^5 dx

    Now normally I find these questions relatively easy, where all the values under the square root are substituted for u.

    This question does not seem to work the same way since du = 3x^2 dx or x^2=du/3

    Clearly this will not replace the  x^5 term outside the square root.


    Any ideas? :-)
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  2. #2
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    Quote Originally Posted by fityfity View Post
    Hi there. I'm new here :-)

    I've been going through a fair few substitution questions, but I have been stumped on this one.

    I have to solve the following by substitution:
    <br />
\int \sqrt{x^3+1} *  x^5 dx

    Now normally I find these questions relatively easy, where all the values under the square root are substituted for u.
    Yes, exactly right. Let u= x^3+ 1

    This question does not seem to work the same way since du = 3x^2 dx or x^2=du/3
    Yes, and x^5dx= x^3(x^2dx)= (u- 1)du/3.

    Clearly this will not replace the  x^5 term outside the square root.


    Any ideas? :-)
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  3. #3
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    Ahh that makes so much sense

    It always appears easy once someone shows you

    Thank you very much for your help
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