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Math Help - integration partial fractions

  1. #1
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    integration partial fractions

    integral of (u+4)/((u^2)+4) du

    How would I solve for this?
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by khuezy View Post
    integral of (u+4)/((u^2)+4) du

    How would I solve for this?
    THere is no need for partial fractions here

    \int\frac{u+4}{u^2+4}du=\int\frac{u}{u^2+4}du+4\in  t\frac{du}{u^2+4}=\frac{1}{2}\ln|u^2+4|+2\arctan\b  igg(\frac{u}{2}\bigg)+C


    Also, conider the fact that if you wanted to do this by partial fractions the denominators factorization would be imaginary

    And even if it is too hard to learn LaTeX a useful command is alt 0178 gives
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  3. #3
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    Since u^2+4 is positive for all u, we can remove the absolute value bars.
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  4. #4
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Krizalid View Post
    Since u^2+4 is positive for all u, we can remove the absolute value bars.
    Thanks Krizalid, that is a good point. I just automatically did it...better than what I usually do and don't put them at all
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