2. (a) (c) 1 x-5x+6 Evaluate - S In x-31 - In/x-2| + C In x-3| + In|x-2| + C -dx (b) (d) (In/x-3)(In/x-2) + C In/x-21-In/x-31+ C

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Problem 2:**

Evaluate the integral:

\[
\int \frac{1}{x^2 - 5x + 6} \, dx
\]

**Options:**

(a) \(\ln|x-3| - \ln|x-2| + C\)

(b) \((\ln|x-3|)(\ln|x-2|) + C\)

(c) \(\ln|x-3| + \ln|x-2| + C\)

(d) \(\ln|x-2| - \ln|x-3| + C\)

**Solution Guide:**
To solve this integral, consider factoring the quadratic expression in the denominator \(x^2 - 5x + 6\) into \((x-3)(x-2)\) and use partial fraction decomposition.
Transcribed Image Text:**Problem 2:** Evaluate the integral: \[ \int \frac{1}{x^2 - 5x + 6} \, dx \] **Options:** (a) \(\ln|x-3| - \ln|x-2| + C\) (b) \((\ln|x-3|)(\ln|x-2|) + C\) (c) \(\ln|x-3| + \ln|x-2| + C\) (d) \(\ln|x-2| - \ln|x-3| + C\) **Solution Guide:** To solve this integral, consider factoring the quadratic expression in the denominator \(x^2 - 5x + 6\) into \((x-3)(x-2)\) and use partial fraction decomposition.
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