# How to do intgral for (cos(x)^2)*cos(wx)

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1. Dec 20, 2015

### mirshayan

• Member warned about posting with no effort shown
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Dec 20, 2015

### mirshayan

excuse me
i want integral of cos(x^2)*cos(wx)dx

3. Dec 20, 2015

### Samy_A

I "want" that too.

1. Are you sure that is the exercise? No typo?

4. Dec 20, 2015

### mirshayan

actually its the Fourier cos transforms of cos(x^2)
our teacher ask us To prove it. i know the answer is what (see the attach file) but i want way

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5. Dec 20, 2015

### Samy_A

There are probably a number of ways to prove it.

I would start by noting that $\cos (y)=\frac{e^{iy}+e^{-iy}}{2}$.

But show us how you would try to find the answer, please.
Remember that the real question is not to find the integral of $\cos(x²)\cos(\omega x)$, but to find the Fourier transform of $\cos(ax²)$. You could at least start by defining that Fourier transform in the "relevant equations" part of the template.

6. Dec 20, 2015

thx alot