# How do I integrate this?

1. May 24, 2014

### Mathmanman

∫sin(x^3) dx

I have absolutely no clue on what to deal with the x^3 part.
All I can think of is this:
∫sin(ax) dx = -1/a cos(ax) + C

2. May 24, 2014

### micromass

There is no solution in terms of elementary functions. You need either the incomplete Gamma function or the exponential integral.

3. May 24, 2014

### Mathmanman

Can you give me the link to Gamma function or the exponential integral?

So if a teacher were to give me that problem, I could say: "there is no solution"?

4. May 24, 2014

### micromass

5. May 24, 2014

### Mathmanman

I'm sorry but wikipedia is hard to read and I can't get the main point when reading wikipedia on math.
Can you explain it if you can?

6. May 24, 2014

### micromass

Can I explain what exactly?

7. May 24, 2014

### Mathmanman

8. May 25, 2014

### HomogenousCow

Just look at the definition for the special functions.
With appropriate substitution and manipulation you can get your integral into something which can be expressed in terms of those special functions.

9. May 28, 2014

### Kainui

Although not pretty, you could convert it to a taylor series by using the one for sin(x) and simply plug in x^3.

10. May 30, 2014