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Math Help - Two integrals giving me a hard time

  1. #1
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    Two integrals giving me a hard time

    The first one is:

    \int x^5 ln(1+x^3) dx

    The second is:

    \int_0^1 \frac {1}{(16+x^2)^2}dx

    For both problems I used parts but the problems got quite ugly so I stopped. I was wondering if there are any rules or methods I am missing that would make these problems easier
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  2. #2
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    The first can be solved integrating by parts and then performing a substitution.

    The second contains an expression of the form a^2+x^2. Try substituting x=a\tan u.
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  3. #3
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     \int x^5 log(1 + x^3)  dx = \int x^2  log(1 + x^3)  x^3 dx so use the substitution  u = x^3 .

    I haven't tried to work out the second one yet, but when I look at it, the substitution  u = 4tan(x) jumps out at me.
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  4. #4
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    I'm still having trouble on both. On the first integral I've substituted u=x^3 then I did parts and got stuck. On the second one I did trig sub but I get stuck when you plug the original variables back in (what does arctan \frac {1}{4} equal?). Thanks for both your help so far, but I still need a little bit more help.
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  5. #5
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    So I think I solved the first one but the second one is still giving me some trouble when it comes to substituting the bounds back in.
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