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Math Help - Need some help starting a def integral!

  1. #1
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    Need some help starting a def integral!

    I need to integrate \int arctan(1/x) dx from 1 to \sqrt{3}. If someone could please show me the first few steps, like the substitutions, that would be great!
    Thanks
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: Need some help starting a def integral!

    Have you tried with integration by parts?
    \int_{1}^{\sqrt{3}} \arctan\left(\frac{1}{x}\right)dx=\left[\arctan\left(\frac{1}{x}\right)\cdot x\right]_{1}^{\sqrt{3}}-\int_{1}^{\sqrt{3}} d\left[\arctan\left(\frac{1}{x}\right)\right]\cdot x
    =\left[\arctan\left(\frac{1}{x}\right)\cdot x\right]_{1}^{\sqrt{3}}+\int_{1}^{\sqrt{3}} \frac{x}{x^2+1}dx

    For the last integral you just have to use a simple substitution.
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  3. #3
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    Re: Need some help starting a def integral!

    Oh, okay! So u=arctan(1/x) and dv=dx. It all makes sense now, thanks!
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  4. #4
    MHF Contributor Siron's Avatar
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    Re: Need some help starting a def integral!

    Quote Originally Posted by NeedDirection View Post
    Oh, okay! So u=arctan(1/x) and dv=dx. It all makes sense now, thanks!
    Indeed! I think you can figure out the last integral .
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