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Math Help - integral2

  1. #1
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    Question integral2

    integral

    du/(sqrt(1+u^2) )

    any help pls
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  2. #2
    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by alex83 View Post
    integral
    <br />
\int \frac{du}{\sqrt{1+u^2}}

    any help pls
    You can find this in a table of integrals. It's arcsinh(u). (It's the "inverse hyperbolic sine of u".)
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  3. #3
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    Quote Originally Posted by alex83 View Post
    integral

    du/(sqrt(1+u^2) )

    any help pls
    As you'll see this is a standard trig integral, but it's better to do it by trig substitution.

    Construct a right triangle with a vertical leg of u, a horizontal leg of 1 and by Pythagoras the hypotenuse is \sqrt{1+u^2}. Let theta be the angle such that \tan(\theta)=u. You will also notice that \cos(\theta)=\frac{1}{\sqrt{1+u^2}}, which makes an easy substitution. Make sure to calculate d\theta in terms of u, then make the full substitution, integrate, then back substitute.
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  4. #4
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    a classic problem, we can also put v=u+\sqrt{1+u^2}.
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