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\[\int\limits_0^{2 pi} (\sqrt{1/(3 pi)}+e^{i x}\sqrt{1/(6 pi)} )^2 dx = 2/3 \]

The inside is squared.

The e^ix is really bugging me.

\[\int\limits_0^{2\pi}\sqrt{\frac{1}{3\pi}}+e^{ix}\sqrt{\frac{1}{{(6\pi)}^2}}\text d x=\frac 2 3\]

is that right?

no no The whole thing inside the integral is squared.

yes yes.

So do I just foil it out and find the integral?

turn e^(ix) into cos x+i sin x.

Then, replace the g's back with i's. Remember that i^2=-1

tried that

My calc 2 teacher avoided imaginary numbers. So I'm really curious now.

Mathematica is on my dead mac... Ugh

Anyone have Mac OS X up. Grapher could probably do it.

Change it to polar form maybe?

what do i enter into grapher?
@Christbot

You guys familiar with Euler's formula?

Yes but I don't need to use it at this point.

That was the original problem I just wrote it wrong.

Ouch!

Ouch indeed I hate my life right now. lol

shouldn't post your phone number on the internet lol and I don't have an iphone. :(

I'm just facebooking myself the input... I'll work to copy and paste, lol

What the hell?! Wolfram won't integrate it?!

Can't we let 1 = trig identity? Wow...

bam I got it as an indefinite integral! Gotta wait for my slow phone, sorry!

TY!!

Want the last bit or you got it?

Go it!

High five!

*high five*
thanks again!! really helped me out!

No prob! I love a good problem.

Oh the web version works for free. Yeah, sometime you just gotta tinker with the input. I'm deleting the image links, but here is my mathy blog, FWIW http://mathstem.blogspot.com/ I'll delete my cell# too, lol!