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

1. Aug 2, 2010

### esisk

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

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

2. Aug 2, 2010

### Char. Limit

Re: Integration

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).

3. Aug 3, 2010

### HallsofIvy

Re: Integration

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

4. Aug 3, 2010

### Char. Limit

Re: Integration

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.

5. Aug 4, 2010

6. Aug 4, 2010

### HallsofIvy

Re: Integration

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

7. Aug 18, 2010

### tauchatri

Re: Integration

hey this function is not integerable

8. Aug 18, 2010

### HallsofIvy

Re: Integration

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

9. Aug 19, 2010

### tauchatri

Re: Integration

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

10. Aug 19, 2010

### Char. Limit

Re: Integration

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.