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Math Help - Integral techniques

  1. #1
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    Integral techniques

    The problem im working on right now is the integral of xarcsinx dx
    I tried using integration by parts but that gets me no where. if anyone could point me in the right direction to get me started it would be mucho appreciated.
    also the integral of (x^4)(lnx) dx I tried using integration by parts setting u = lnx and dv = x^4dx but my teacher tells me my answer is incorrect. any suggestions will help thank you !
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  2. #2
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    #1) Let u=arcsin(x) and dv=x. The integral of vdu can be solved by u-substitution.

    #2) That is the right idea. Show us your work so we can spot the error.
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  3. #3
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    K thank you! alright well I have the integral x^4lnxdx = lnx*(1/5)x^5 - integral (1/5)x^5 * (1/x) dx which i simplified to (1/5)(lnx)(x^5) - (1/5)integral (x^4) dx
    and from there I solved for the integral and came up with (1/5)(lnx)(x^5) - (1/10)(x^5) + C

    thanks again for your help
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