# Integrating Sin(x^3) - Homework Equations & Solution

• Hybrid_Theory
In summary, the basic equations for integrating Sin(x^3) include ∫sin(x^3)dx = -1/3cos(x^3) + C. To solve these integrals, you can use the substitution method, integration by parts, or trigonometric identities. There is also a specific technique called the Fresnel integral that involves using complex numbers and the Gamma function. To verify the solution of an integral involving Sin(x^3), you can differentiate the solution and check if it gives the original function. While calculators or computer software can be used to solve these integrals, it is important to understand the steps and techniques used for accuracy.
Hybrid_Theory

## Homework Statement

I need to intergrate sin(x^3) for a sum and I don't know how to.

## Homework Equations

The sum is (integrate)3x+Sin(x^3)+1

## The Attempt at a Solution

I've tried substituting u for x^3 but I don't know where to go from there considering du=3x^2.dx, which isn't relevant to my equation in any way.

You are not going to find any elementary function anti-derivative for this.

That's what I figured. So what do I do with it?

## 1. What are the basic equations for integrating Sin(x^3)?

The basic equation for integrating Sin(x^3) is given by ∫sin(x^3)dx = -1/3cos(x^3) + C, where C is the constant of integration.

## 2. How do you solve integrals involving Sin(x^3)?

To solve integrals involving Sin(x^3), you can use the substitution method by letting u = x^3 and then solving the integral as ∫sin(u)du. You can also use integration by parts or trigonometric identities to simplify the integral before solving.

## 3. Is there a specific technique for integrating Sin(x^3)?

Yes, there is a specific technique for integrating Sin(x^3) known as the Fresnel integral. It involves using complex numbers and the Gamma function to solve the integral.

## 4. How do you verify the solution for an integral involving Sin(x^3)?

You can verify the solution for an integral involving Sin(x^3) by differentiating the solution and checking if it gives the original function. In this case, the derivative of -1/3cos(x^3) is sin(x^3), so the solution is verified.

## 5. Can you use a calculator to solve integrals involving Sin(x^3)?

Yes, you can use a calculator or a computer software to solve integrals involving Sin(x^3). However, it is important to understand the steps and techniques used in solving the integral to ensure the accuracy of the result.

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