Integrate (√(1+x^2))/(x))

I get to the integral of 1/(sinxcos²x)

What would I do next

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- Oct 13th 2010, 09:52 PMandrewho93Trig Substitution
Integrate (√(1+x^2))/(x))

I get to the integral of 1/(sinxcos²x)

What would I do next - Oct 13th 2010, 10:11 PMyannyy
use u=cosx and then do another trig substitution if you get stuck.

- Oct 13th 2010, 10:50 PMTheCoffeeMachine
Without a trigonometric substitution, doing in this way yields a very nice answer:

[LaTeX ERROR: Convert failed] " alt=" \displaystyle = \int\frac{u^2}{(u+1)(u-1)}\;{du} = \int \left\{\frac{1}{2(u-1)}-\frac{1}{2(u+1)}+1 \right\}\;{du}[/tex] [LaTeX ERROR: Convert failed] " />[LaTeX ERROR: Convert failed]

Quote:

I get to the integral of 1/(sinxcos²x)

What would I do next

- Oct 13th 2010, 10:55 PMyannyy
oh that's a very smart hint

- Oct 14th 2010, 08:09 AMKrizalid
i like when trig. is not everything, here's another way to tackle it:

consider substitute and the integral becomes back substitute and get