How do I integrate sin(x^2) please? Not (sin(x))^2.

[esisk]

How do I integrate sin(x^2) please?

Not (sin(x))^2. Thanks again

 

[Char. Limit]

Use a certain equality of the sine function, namely...

sin(u) = \frac{e^{iu}-e^{-iu}}{2i}

Replace u with x^2 and you're good to go, assuming you know erf(x) and erfi(x).

 

[HallsofIvy]

In other words, the integral cannot be done in terms of elementary functions.

 

[Char. Limit]

In other words, the integral cannot be done in terms of elementary functions.

But that's true for most integrals. I used to freak out when I couldn't solve an integral in terms of elementary functions, but I know better now.

 

[JJacquelin]

http://mathworld.wolfram.com/FresnelIntegrals.html

 

[HallsofIvy]

But that's true for most integrals. I used to freak out when I couldn't solve an integral in terms of elementary functions, but I know better now.

Actually, it is true for "almost all" functions!

 

[tauchatri]

How do I integrate sin(x^2) please?

Not (sin(x))^2. Thanks again

hey this function is not integerable

 

[HallsofIvy]

How do I integrate sin(x^2) please?

Not (sin(x))^2. Thanks again

hey this function is not integerable

Non-sense. It is continuous, therefore it is integrable. It is simply not integrable in terms of elementary functions.

 

[tauchatri]

Non-sense. It is continuous, therefore it is integrable. It is simply not integrable in terms of elementary functions.

i only mean that you duffer.it's not easy to integrate

 

[Char. Limit]

i only mean that you duffer.it's not easy to integrate

Difficulty really shouldn't matter with integration, I mean, this function isn't easy to integrate either:

\frac{sin(x^2) tan(x^3)}{x}+3 x^2 log(x) sin(x^2) sec^2(x^3)+2 x log(x) cos(x^2) tan(x^3)

But we can still express the integral in terms of elementary functions.