Math Problem Statement
∫▒x/〖(x^2-1)〗^2 dx=
Solution
To solve the integral , we can use the substitution method. Let's go through the steps:
-
Substitution: Let . Then, or .
-
Rewrite the integral: Substituting and into the integral: The terms cancel out:
-
Integrate: The integral now is: Using the power rule for integration , we get:
-
Substitute back: Replace with :
So, the solution to the integral is:
Would you like any further details or have any questions?
Here are 5 questions you might want to ask next:
- How do you solve a definite integral for a similar function?
- Can you explain the substitution method in more detail?
- How do you handle integrals with different forms of rational functions?
- What are some common techniques for integrating rational functions?
- Can you provide examples of more complex integrals and their solutions?
Tip: Always check if substitution or partial fraction decomposition can simplify the integration process.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Integration
Substitution Method
Rational Functions
Formulas
Integration by substitution
Theorems
-
Suitable Grade Level
Advanced High School and Above
Related Recommendation
Step-by-Step Solution for Integrating x/(x+1)^2
Integration of Rational Function \( \int \frac{2x}{(x - 1)^2} \, dx \) Using Substitution
Integral of -2x/(x^2-x+1): Step-by-Step Solution
Solve the Integral ∫(1 + x^2)/(1 + 2x) dx - Step-by-Step Solution
Solve \(\int \frac{1}{\left(x+2\right)^2} \, dx\) using Substitution Method