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Math Help - definite integral

  1. #1
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    definite integral

    find the indefinite integral of x/(1+x^4)

    Let u = x^2; then du = 2x dx, so

    ∫ x dx /(1+x^4) = (1/2) ∫ 2x dx / (1+x^4) = (1/2) ∫ du / (1 + u^2)......blanked out

    ans: arctan (x^2)/2....huh??
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by Taurus3 View Post
    find the indefinite integral of x/(1+x^4)

    Let u = x^2; then du = 2x dx, so

    ∫ x dx /(1+x^4) = (1/2) ∫ 2x dx / (1+x^4) = (1/2) ∫ du / (1 + u^2)......blanked out

    ans: arctan (x^2)/2....huh??
    You are good so far now make the trig sub

    u=\tan(\theta) \implies du =\sec^2{\theta}d\theta and remember that

    \tan^2(\theta)+1=\sec^2{\theta}
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  3. #3
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    hold, on. I don't get what you mean.
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  4. #4
    Behold, the power of SARDINES!
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    Quote Originally Posted by Taurus3 View Post
    hold, on. I don't get what you mean.
    just plug in what I suggested to get

    \displaystyle \frac{1}{2} \int \frac{du}{1+u^2}=\frac{1}{2} \int \frac{\sec^2(\theta)}{1+\tan^2(\theta)}d\theta=\fr  ac{1}{2} \int d\theta=\frac{\theta}{2}=\frac{1}{2}\tan^{-1}(u)=...
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  5. #5
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    oh dumb....thanks haha.
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