How do I integrate this?

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In summary: 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.
  • #1
Mathmanman
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∫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
 
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  • #2
There is no solution in terms of elementary functions. You need either the incomplete Gamma function or the exponential integral.
 
  • #3
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
  • #5
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
Mathmanman said:
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?
 
  • #7
More like translate the wikipedia pages you posted into english that people can actually read.
 
  • #8
Mathmanman said:
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.
 
  • #9
Although not pretty, you could convert it to a taylor series by using the one for sin(x) and simply plug in x^3.
 

1. How do I integrate this function?

To integrate a function, you must first identify the variable of integration. Then, use the appropriate integration rules, such as the power rule or substitution, to integrate the function. Finally, add a constant of integration to the result.

2. Is there a specific method for integration?

There are several methods for integration, such as the power rule, substitution, integration by parts, and trigonometric substitution. The method used depends on the complexity of the function being integrated.

3. Can I integrate without knowing the limits?

In some cases, yes, you can integrate without knowing the limits. This is known as indefinite integration and results in a general solution with a constant of integration. However, for definite integration, you need to know the limits of integration to find a specific solution.

4. What is the difference between definite and indefinite integration?

Definite integration involves finding the area under a curve between two specific limits. It results in a specific numerical value. Indefinite integration, on the other hand, involves finding the antiderivative of a function without specific limits, resulting in a general solution with a constant of integration.

5. Are there any common integration mistakes to avoid?

Some common integration mistakes include forgetting to add the constant of integration, not properly identifying the variable of integration, and making algebraic errors. It is important to double-check your work and be familiar with the integration rules to avoid these mistakes.

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