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Math Help - How do I start this problem?

  1. #1
    Newbie
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    How do I start this problem?

    \int \frac{xtan^-1 } {sqrt 1+x^2} dx


    I'm pretty sure I have to find uv, v, du and u, but I'm having some trouble with it. Tried trigonometric substitution but it doesn't seem to be working. any help would be appreciated

    hope the problem's understandable
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  2. #2
    Math Engineering Student
    Krizalid's Avatar
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    Yes, integration by parts will make this easier, we have

    \int{\frac{x\arctan x}{\sqrt{1+x^{2}}}\,dx}=\sqrt{1+x^{2}}\arctan x-\int{\frac{\sqrt{1+x^{2}}}{1+x^{2}}\,dx}, and as for the computation for last integral we have \int{\frac{\sqrt{1+x^{2}}}{1+x^{2}}\,dx}=\int{\fra  c{dx}{\sqrt{1+x^{2}}}}, and put t=x+\sqrt{x^2+1} to finish the problem.
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  3. #3
    MHF Contributor Calculus26's Avatar
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    is the pblm xarctan(x)/sqrt(x^2+1)

    0r xarctan(sqrt(x^2+1)) ?

    if the pblm is xarctan(sqrt(x))

    See attachment
    Attached Thumbnails Attached Thumbnails How do I start this problem?-helluvaanintgrl.jpg  
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