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Thread: Pretty simple Calculus questions

  1. #1
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    Pretty simple Calculus questions

    Hello. First post on this forum. I have an assortment of questions, hope somebody can help me.
    first: $\displaystyle \int \frac{1}{x^3+x} dx$

    second: $\displaystyle \int \sqrt{1-x^2} dx $

    third: $\displaystyle \int$$\displaystyle \frac{1}{ sin^2 cot^3} dx$

    a hand on these will be very appreciated
    Last edited by Corum; Jan 6th 2010 at 03:02 PM. Reason: LaTeX
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  2. #2
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    Quote Originally Posted by Corum View Post
    Hello. First post on this forum. I have an assortment of questions, hope somebody can help me.
    first: $\displaystyle \int_ (1/x^3+x) dx$

    second: $\displaystyle \int$ (1-x^2)^(1/2)dx (that's trying to be a sqr root)

    third: $\displaystyle \int$(sin^-3 x / cot^3) dx

    $\displaystyle \int \frac{1}{x(x^2+1)} \, dx$

    partial fractions


    $\displaystyle \int \sqrt{1-x^2} \, dx$

    try a trig sub ... $\displaystyle x = \sin{\theta}$


    $\displaystyle \int \frac{\sin^{-3}{x}}{\cot^3{x}} \, dx
    $

    use a some trig identities ...

    $\displaystyle \frac{\sin^{-3}{x}}{\cot^3{x}} = \sec^3{x}$

    $\displaystyle \int \sec^3{x} \, dx$

    use parts ... $\displaystyle u = \sec{x}$ , $\displaystyle dv = \sec^2{x} \, dx$
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