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Expert-verified Found in: Page 334 ### Essential Calculus: Early Transcendentals

Book edition 2nd
Author(s) James Stewart
Pages 830 pages
ISBN 9781133112280 # Evaluate the integral: $$\int {\frac{{axdx}}{{{x^2} - bx}}}$$

Hence, the value of $$\int {\frac{{axdx}}{{{x^2} - b}}}$$ is $$a\log \left| {x - b} \right| + c$$

See the step by step solution

## Step 1: Factorizing

$$\int {\frac{{axdx}}{{{x^2} - bx}}} = \int {\frac{{axdx}}{{x(x - b)}} = \int {\frac{{adx}}{{x - b}}} }$$

## Step 2: Finding value

$$\int {\frac{{adx}}{{x - b}}}$$

Let $$x - b = v$$

$$\begin{array}{l}1 = \frac{{dv}}{{dx}}\\ \Rightarrow dx = dv\\ \Rightarrow a\int {\frac{{dv}}{v} = a\log \left| v \right|} + c\\ = a\log \left| {x - b} \right| + c\end{array}$$

Hence, the value of $$\int {\frac{{axdx}}{{{x^2} - b}}}$$ is $$a\log \left| {x - b} \right| + c$$ ### Want to see more solutions like these? 