Short Answer

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 by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

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

Find Study Materials for

Create Study Materials

Select your language

Essential Calculus: Early Transcendentals

Answers without the blur.

Short Answer

Evaluate the integral: \(\int {\frac{{axdx}}{{{x^2} - bx}}} \)

Step by Step Solution

Step 1: Factorizing

Step 2: Finding value

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Select your language

Essential Calculus: Early Transcendentals

Answers without the blur.

Short Answer

Evaluate the integral: \(\int {\frac{{axdx}}{{{x^2} - bx}}} \)

Step by Step Solution

Step 1: Factorizing

Step 2: Finding value

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Probability and Statistics

Statistics

Mechanics Maths

Geometry

Pure Maths