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Q13E

Expert-verifiedFound in: Page 334

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 \(a\log \left| {x - b} \right| + c\)

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

\(\int {\frac{{adx}}{{x - b}}} \)

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 \(a\log \left| {x - b} \right| + c\)

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