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$\int_0^\frac{\pi}{4} \! \frac{1+\cos^2\theta}{\cos^2\theta} d\theta$

I've been attempting to mix and match identities to make this equation easier to integrate.

Mathematica has given me an answer of $\frac{4 + \pi}{4}$, so I'm trying to get there but am struggling.

Any suggestions? Thanks

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    If you do in WolframAlpha what you did in Mathematica, you can click "show steps" and it will show you the steps. By the way, you're still missing a $\mathrm{d}\theta$.2011-03-31

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Just divide: $\int \frac{1+\cos^2 \theta}{\cos^2 \theta} \, d\theta = \int ( \sec^2 \theta + 1 ) \, d\theta $ and go from there.

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    Ah, that got me looking at my notes again. I in fact went the long way to get $\sec^2\theta$ and was so happy that I could convert it to $\tan\theta$ that I omitted the trailing $\theta$ after integrating. Seems to work now. Thanks2011-04-01