Integration by Substitution Questions
1. [Tex]\int 2x \cos(x^2) \, dx [/Tex]
2. [Tex]\int \sin(3x) \cos(3x) \, dx[/Tex]
3. [Tex]\int x e^{x^2} \, dx[/Tex]
4. [Tex]\int \frac{2x}{x^2 + 1} \, dx[/Tex]
5. [Tex]\int \frac{\sin(x)}{\cos^3(x)} \, dx[/Tex]
6.[Tex] \int (3x^2 – 5)^5 \cdot 6x \, dx[/Tex]
Integration by Substitution Method
Integration by substitution is one of the important methods for finding the integration of the function where direct integration can not be easily found. This method is very useful in finding the integration of complex functions. We use integration by substitution to reduce the given function into the simplest form such that its integration is easily found.
In calculus, integration by substitution is a method used to solve integrals and antiderivatives, also referred to as u-substitution, the reverse chain rule, or change of variables. It serves as the analog to the chain rule used in differentiation. Essentially, this method can be viewed as the chain rule in reverse to simplify and evaluate integrals.
Now let’s learn more about the integration by substitution method, Integration by Substitution examples, and others in this article.
Table of Content
- What Is Integration by Substitution?
- Integration by Substitution Method
- When to use Integration by Substitution?
- Steps to Integration by Substitution
- Integration by Substitution – Important Substitutions
- Integration by Substitution Examples
- Integration by Substitution Questions
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