How Can I Integrate the Function ∫sin(x^3) dx?

[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

 

[micromass]

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

 

[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"?

 

[micromass]

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"?

There is a solution. The integral certainly exists and defines a function. You just can't describe the function in terms of elementary functions such as sines, cosines, square roots, logarithms, etc.

http://en.wikipedia.org/wiki/Incomplete_gamma_function
http://en.wikipedia.org/wiki/Exponential_integral

 

[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?

 

[micromass]

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?

Can I explain what exactly?

 

[Mathmanman]

More like translate the wikipedia pages you posted into english that people can actually read.

 

[HomogenousCow]

More like translate the wikipedia pages you posted into english that people can actually read.

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.

 

[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.

 

[athosanian]

http://integrals.wolfram.com/index.jsp?expr=Sin[x^3]&random=false

use this , wolframe online integrator