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Math Help - Intergration at SIGHT !?!?!?!?!?

  1. #1
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    Intergration at SIGHT !?!?!?!?!?

    Firsty i dont know what intergration at sight means, and here is the question:

    By Intergrating at sight, find:

    1. \int x^3. ({x^4}+4)^2  dx

    2. \int \sin\theta \sqrt{1-\cos\theta}  d\theta

    3. \int x.e^{x^2 + 1}   dx

    4. \int e^x. (1-e^x)^3  dx

    5. \int (x + 1). \sqrt{x^2 + 2x + 3} dx
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  2. #2
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    Quote Originally Posted by Stylis10 View Post
    Firsty i dont know what intergration at sight means,
    It means that looking at the problem we see basic forms.
    In #1 we see a form of u^2 du.

    In #2 we see a form of \sqrt{u} du.

    In #3 we see a form of e^u du.
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  3. #3
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    Quote Originally Posted by Stylis10 View Post
    Firsty i dont know what intergration at sight means, and here is the question:

    By Intergrating at sight, find:

    1. \int x^3. ({x^4}+4)^2  dx

    2. \int \sin\theta \sqrt{1-\cos\theta}  d\theta

    3. \int x.e^{x^2 + 1}   dx

    4. \int e^x. (1-e^x)^3  dx

    5. \int (x + 1). \sqrt{x^2 + 2x + 3} dx
    EDIT: With practice, you will be able to spot some integration by sight. Mainly, the chain rule is the one that can be differentiated and integrated by sight easily.

    1)
    \frac{1}{12}(x^4 + 4)^3

    2)
    \frac{2}{3} (1 - cos \theta)^\frac{3}{2}

    3)
    \frac{1}{2}e^{x^2 +1}

    4)
    -\frac{1}{4}(1 - e^x)^4

    5)
    \frac{1}{3}(x(x+2) + 3)^{\frac{3}{2}}
    Last edited by Simplicity; March 9th 2008 at 09:56 AM.
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  4. #4
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    im still clueless, reply to plato

    thank you AIR, i was trying to use the intergration product rules once ofund out u were supposed to do it in your head, but the chain rule makes more sense
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