Substitution in Indefinite Integral

Thread starter phillyolly
Start date Jul 22, 2010
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Indefinite Indefinite integral Integral Substitution

In summary, substitution in indefinite integral is a technique used to simplify integrals by replacing a variable with a function or expression. It should be used when the integrand contains a function that can be replaced with a simpler function. To perform substitution, the variable and function are identified, the integral is rewritten, the derivative is substituted, and then the integral is simplified and solved. The main benefit of using substitution is that it can make difficult integrals easier to solve, but there are limitations such as it may not work for all integrals and multiple substitutions may be required.

Jul 22, 2010

phillyolly

Homework Statement

I started the problem, got stuck.

Homework Equations

The Attempt at a Solution

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Jul 22, 2010

jegues

Take the constants out of the integral and solve,

[tex]\frac{1}{2}\int \frac{du}{1 + u^{2}} = \frac{1}{2}tan^{-1}(u) + C [/tex]

Since,

[tex] u = x^{2} [/tex]

Then,

[tex]\frac{1}{2}tan^{-1}(u) + C = \frac{1}{2}tan^{-1}(x^{2}) + C[/tex]

Jul 22, 2010

phillyolly

Oh snap, that was easy.
Thank you!

Related to Substitution in Indefinite Integral

1) What is substitution in indefinite integral?

Substitution in indefinite integral is a technique used to solve integrals by replacing a variable with a function or expression in order to simplify the integral and make it easier to solve.

2) When should we use substitution in indefinite integral?

Substitution should be used when the integrand (the expression inside the integral) contains a function that can be replaced with a simpler function by using a substitution.

3) How do we perform substitution in indefinite integral?

To perform substitution in indefinite integral, we follow these steps:

1. Identify the variable to be substituted and the function to be used in the substitution.

2. Rewrite the given integral in terms of the new variable and function.

3. Find the derivative of the new variable and substitute it into the integral, along with the new function.

4. Simplify the integral and integrate it as usual.

4) What are the benefits of using substitution in indefinite integral?

The main benefit of using substitution in indefinite integral is that it can simplify the integral and make it easier to solve. It can also help to solve integrals that may be difficult or impossible to solve using other techniques.

5) Are there any limitations to using substitution in indefinite integral?

Yes, there are some limitations to using substitution in indefinite integral. It may not work for all integrals, and sometimes it may not lead to a simpler integral. In some cases, multiple substitutions may be required to solve the integral.