1. ## Trigonometric Integration

Could someone please explain how to integrate:

∫ x sin2(x) cos2(x2) dx

Using trigonometric integration?

[updated]

3. ## Re: Trigonometric Integration

Originally Posted by MaxJasper
$\frac{1}{128} \left[8 x^2-4 x \sin (4 x)-\cos (4 x)\right]$
That's wrong.

4. ## Re: Trigonometric Integration

Originally Posted by Preston019
That's wrong.
It is not nice. But here it is.

5. ## Re: Trigonometric Integration

$\frac{1}{32} \left(-\sqrt{\pi } \cos \left(\frac{1}{2}\right) C\left(\frac{2 x-1}{\sqrt{\pi }}\right)+\sqrt{\pi } \cos \left(\frac{1}{2}\right) C\left(\frac{2 x+1}{\sqrt{\pi }}\right)-\sqrt{\pi } \sin \left(\frac{1}{2}\right) S\left(\frac{2 x-1}{\sqrt{\pi }}\right)+\sqrt{\pi } \sin \left(\frac{1}{2}\right) S\left(\frac{2 x+1}{\sqrt{\pi }}\right)+4 x^2+2 \sin \left(2 x^2\right)-4 x \sin (2 x)-\sin (2 (x-1) x)-\sin (2 x (x+1))-2 \cos (2 x)\right)$

6. ## Re: Trigonometric Integration

Originally Posted by Preston019
Could someone please explain how to integrate:

∫ x sin2(x) cos2(x2) dx

Using trigonometric integration?

First of all, I'm not sure what you mean by "trigonometric integration", but I am assuming that the OP has written the original question wrongly, considering the difficulty of the solution.

7. ## Re: Trigonometric Integration

Originally Posted by Prove It
First of all, I'm not sure what you mean by "trigonometric integration", but I am assuming that the OP has written the original question wrongly, considering the difficulty of the solution.
Well, maybe you should look in a calculus 2 textbook and you will see that there's a whole section dedicated to "trigonometric integration" with most, if not all, of the solutions being as, or more, "difficult", as you would say, than this one. How did you get title of "MHF Expert" and make a completely idiotic remark like that? That seems like it is the very opposite of "expert."

8. ## Re: Trigonometric Integration

Perhaps you are referring to trigonometric substitution? I can assure you though that the integral you posted is considerably difficult, much more advanced than Calculus 2. Don't forget that even an extra or missing x can complicate an expression unimaginably, maybe you missed one?

9. ## Re: Trigonometric Integration

Originally Posted by SworD
Perhaps you are referring to trigonometric substitution? I can assure you though that the integral you posted is considerably difficult, much more advanced than Calculus 2. Don't forget that even an extra or missing x can complicate an expression unimaginably, maybe you missed one?
Maybe, I'm not sure. Every calc 2 prof. at my university calls it trigonometric integration. The textbook even calls it that. And I just saw that the sin^2(x) is wrong; it's supposed to be sin^2(x^2) my bad

10. ## Re: Trigonometric Integration

Originally Posted by Preston019
Well, maybe you should look in a calculus 2 textbook and you will see that there's a whole section dedicated to "trigonometric integration" with most, if not all, of the solutions being as, or more, "difficult", as you would say, than this one. How did you get title of "MHF Expert" and make a completely idiotic remark like that? That seems like it is the very opposite of "expert."
What an extremely rude and disrespectful comment to make. I have asked you a pertinent question, seeing as you are unlikely to have heard of the Fresnel C and Fresnel F integrals. It is quite possible you did not write the correct integrand, as a similar integrand could be integrated exactly using substitution.

"Trigonometric integration" simply refers to the integration of trigonometric functions, NOT a METHOD of integration, which is what you were asking for.

11. ## Re: Trigonometric Integration

Make the substitution u = x^2 then possibly refer to the double angle identity for sine, and see if that takes you anywhere.