Integration

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Vikash

Junior Member
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Sep 29, 2020
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62
May i please know the detailed method for intergrating cos(2x2 +3) with respect to x. Thanks.?
 
After 53 prior posts you are going to ask us to solve a problem for you? That is not going to happen.
Please share your work with us and then we will help you get to the correct answer.

Can you please post the exact problem?A picture would be best.
 
It doesn't look like it can be integrated into a closed form using well known functions.

Mathematica returns

[MATH]\displaystyle \int ~\cos(2x^2+3) ~dx = \frac{1}{2} \sqrt{\pi } \left(\cos (3) C\left(\frac{2 x}{\sqrt{\pi }}\right)-\sin (3) S\left(\frac{2 x}{\sqrt{\pi }}\right)\right)[/MATH]
where [MATH]C(x),~S(x)[/MATH] are the Fresnel integrals
 
Romsek said:
It doesn't look like it can be integrated into a closed form using well known functions.

Mathematica returns

[MATH]\displaystyle \int ~\cos(2x^2+3) ~dx = \frac{1}{2} \sqrt{\pi } \left(\cos (3) C\left(\frac{2 x}{\sqrt{\pi }}\right)-\sin (3) S\left(\frac{2 x}{\sqrt{\pi }}\right)\right)[/MATH]
where [MATH]C(x),~S(x)[/MATH] are the Fresnel integrals
Click to expand...
I suspect that he wants the derivative of this (definite) integral. Would you like to make a bet on this?
 
Jomo said:
I suspect that he wants the derivative of this (definite) integral. Would you like to make a bet on this?
Click to expand...

I have no idea what OP wants. All I know is what I read in the papers.
 
I suspect, if you decide to continue with this, that your first step is to break up the cosine into two terms

[MATH]\cos(2x^2+3) = \cos(2x^2)\cos(3) - \sin(2x^2)\sin(3)[/MATH]
I bet with a bit of massaging the integrals of these are the definitions of the Fresnel integrals times a constant.
 
Romsek said:
I have no idea what OP wants. All I know is what I read in the papers.
Click to expand...
I had thought you were expert at:

What OPs want​
​
- including (but not limited to) "= 0"​
 
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