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Math Help - struggling with integration

  1. #1
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    struggling with integration

    Hi can someone please help me with this and explain how you get the answer.

    find the integral of X/(sqrtX^2+4) dx

    any help would be much appreciated.
    Thanks
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: struggling with integration

    I assume you are given:

    \int\frac{x}{\sqrt{x^2+4}}\,dx

    What do you think is a good candidate for a u-substitution?
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  3. #3
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    Re: struggling with integration

    yeah am not really sure where to start with this one.

    i thought that u=sqrtx^2+4 which makes it x+4 correct?
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  4. #4
    MHF Contributor MarkFL's Avatar
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    Re: struggling with integration

    Isn't the entire expression x^2+4 under the radical?

    If so, then try:

    u=x^2+4\:\therefore\:du=2x\,dx

    Is there a way for us to manipulate the integral so that we have a 2x\,dx inside the integral?
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  5. #5
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    Re: struggling with integration

    im sure there is but i cant figure it out at the min. must have missed the part of class where they explained this
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  6. #6
    MHF Contributor MarkFL's Avatar
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    Re: struggling with integration

    Multiply by 2 inside and by 1/2 in front, for a net result of multiplying by 1. So that you have:

    \frac{1}{2}\int\frac{2x}{\sqrt{x^2+4}}\,dx

    Now, using the aforementioned substitution, how may we write this?
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  7. #7
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    Re: struggling with integration

    think i have it 1/2 int 1/sqrt U du

    so answer once you substitute back is sqrt(X^2+4.)+C
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  8. #8
    MHF Contributor MarkFL's Avatar
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    Re: struggling with integration

    Yes, that is correct.
    Thanks from rich1979
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    Re: struggling with integration

    thank you for your help and patience !!!
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  10. #10
    MHF Contributor MarkFL's Avatar
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    Re: struggling with integration

    Glad to help and glad you stuck it out!
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