Math Problem Statement
Use the Log Rule to find the indefinite integral. (Use C for the constant of integration.)
x
x2 + 4
dx
Solution
To solve the indefinite integral using the Log Rule, we recognize that the Log Rule states:
Given the integral:
Step-by-Step Solution:
-
Identify the numerator as the derivative of the denominator (or part of it):
- The denominator is .
- The derivative of is , and we have in the numerator.
-
Rewrite the integral to match the Log Rule format:
-
Apply the Log Rule:
- Here, and .
- So, the integral becomes:
Final Answer:
Would you like a detailed explanation of any step?
5 Related Questions:
- How can the Log Rule be extended to definite integrals?
- What other functions can be solved using the Log Rule?
- How do you handle integrals with explicitly in them?
- Can the Log Rule be used for higher powers in the denominator?
- What substitution methods simplify similar integrals?
Tip: Always check if the derivative of the denominator (or its multiple) appears in the numerator to use the Log Rule effectively!
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Integral Calculus
Logarithmic Integration
Indefinite Integrals
Formulas
Log Rule for Integration: ∫ f'(x)/f(x) dx = ln|f(x)| + C
Theorems
Logarithmic Rule for Integration
Suitable Grade Level
College Calculus or Advanced High School Calculus (Grades 11-12)