Integrating Problem: Solve Questions Using Formula for \int [f(x)]^nf(x)

  • Thread starter ngkamsengpeter
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In summary, the formula for solving integrals of the form ∫ [f(x)]^n f(x) is ∫ [f(x)]^n f(x) dx = (1/(n+1)) [f(x)]^(n+1) + C, where C is the constant of integration. The variable n represents the power to which the function f(x) is raised, and this formula can only be used for functions that are continuous and differentiable on the given interval. The constant of integration, C, is determined by evaluating the integral at a specific point using known values or boundary conditions. While there are other methods for solving integrals of this form, the power rule is often the most efficient and straightforward method.
  • #1
ngkamsengpeter
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Please help me to solve the following questions using [tex]\int [f(x)]^nf(x)=\frac{[f(x)]^{n+1}}{n+1} [/tex]
[tex]\int tan {2x} dx[/tex]
 
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  • #2
What is an integration problem doing in the pre-calculus forum?

Anyway, try writing it as sin over cos, and then use a substitution.
 
  • #3
Are you really asked to use only the power law? Well, I guess you could use Taylor Series.
 

1. What is the formula for solving integrals of the form ∫ [f(x)]^n f(x)?

The formula for solving integrals of this form is ∫ [f(x)]^n f(x) dx = (1/(n+1)) [f(x)]^(n+1) + C, where C is the constant of integration.

2. What does the variable n represent in this formula?

The variable n represents the power to which the function f(x) is raised. This is necessary when the function is not in a form that can be easily integrated using traditional methods.

3. Can this formula be used for any function f(x)?

No, this formula can only be used for functions that are continuous and differentiable on the given interval. Additionally, the function must be in a form that can be raised to a power and integrated.

4. How do I determine the constant of integration, C?

The constant of integration, C, is determined by evaluating the integral at a specific point. This point can be determined by using any known values or boundary conditions given in the problem.

5. Are there any other methods for solving integrals of this form?

Yes, there are other methods such as using substitution or integration by parts. However, the formula for solving integrals using the power rule is often the most efficient and straightforward method.

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