Find the general indefinite integral.

Thread starter phillyolly
Start date Jul 19, 2010
Tags

General Indefinite Indefinite integral Integral

In summary, an indefinite integral is the process of finding the most general antiderivative of a given function, represented by the symbol ∫. It differs from a definite integral in that it has no specific limits of integration and gives a general function instead of a numerical value. The steps for finding the general indefinite integral involve using the power rule, constant multiple rule, and adding a constant of integration. The purpose of finding the general indefinite integral is to find a function whose derivative is equal to the given function and it is also used in various mathematical and scientific problems. In addition, there are techniques such as substitution, integration by parts, trigonometric substitution, and partial fractions that can be used to solve more complex indefinite integrals.

Jul 19, 2010

phillyolly

Homework Statement

Hi! Can anyone check if I got the right answer?

The Attempt at a Solution

Physics news on Phys.org

Jul 19, 2010

snipez90

Looks fine, except the antiderivative of 1/(1+x^2) is inverse tangent, or arctan, sometimes written tan^(-1), but tan^(-2) doesn't make much sense.

Jul 19, 2010

Mark44

Mentor

Insights Author

And whenever you find an antiderivative, it's a good idea to check your work. If you take the derivative of your answer, you should get the integrand.

FAQ: Find the general indefinite integral.

What is an indefinite integral?

An indefinite integral is the process of finding the most general antiderivative of a given function. It is represented by the symbol ∫ and is used to find a function whose derivative is equal to the given function.

What is the difference between an indefinite integral and a definite integral?

The main difference between the two is that a definite integral has specific limits of integration, while an indefinite integral does not. A definite integral also gives a numerical value, while an indefinite integral gives a general function.

What are the steps for finding the general indefinite integral?

The steps for finding the general indefinite integral are:
1. Use the power rule to integrate each term in the function.
2. If necessary, use the constant multiple rule to factor out any constants.
3. Add the constant of integration at the end of the integral. This accounts for all possible antiderivatives of the given function.

What is the purpose of finding the general indefinite integral?

The purpose of finding the general indefinite integral is to find a function whose derivative is equal to the given function. It is also used in finding the area under a curve, as well as solving various mathematical and scientific problems.

Are there any techniques for solving more complex indefinite integrals?

Yes, there are various techniques such as substitution, integration by parts, trigonometric substitution, and partial fractions. These techniques are used to simplify the integral and make it easier to solve.