Alerts Wishlist Cart

Find the integral ∫ (x^2 - 1)/(x - 1) dx.

Practice Questions

Q1
Find the integral ∫ (x^2 - 1)/(x - 1) dx.
  1. (1/3)x^3 - x + C
  2. (1/3)x^3 - x - 1 + C
  3. (1/3)x^3 - x + 1
  4. (1/3)x^3 - x - 1

Questions & Step-by-Step Solutions

Find the integral ∫ (x^2 - 1)/(x - 1) dx.
  • Step 1: Start with the integral ∫ (x^2 - 1)/(x - 1) dx.
  • Step 2: Simplify the expression (x^2 - 1)/(x - 1).
  • Step 3: Notice that x^2 - 1 can be factored as (x - 1)(x + 1).
  • Step 4: Rewrite the integrand: (x^2 - 1)/(x - 1) = ((x - 1)(x + 1))/(x - 1).
  • Step 5: Cancel the (x - 1) terms: you get x + 1.
  • Step 6: Now, the integral becomes ∫ (x + 1) dx.
  • Step 7: Integrate x + 1: ∫ (x + 1) dx = (1/2)x^2 + x + C.
  • Step 8: Write down the final answer: (1/2)x^2 + x + C.
  • Rational Function Integration – The question tests the ability to simplify a rational function before integrating.
  • Polynomial Long Division – Understanding how to divide polynomials is crucial for simplifying the integrand.
  • Basic Integration Techniques – The question assesses knowledge of basic integration rules and techniques.
Biology (School & UG)
Biology (School & UG)
Chemistry (School & UG)
Chemistry (School & UG)
Civil Engineering
Civil Engineering
Commerce & Accountancy
Commerce & Accountancy
Computer Science & IT
Computer Science & IT
Current Affairs & GK
Current Affairs & GK
Data Structures & Algorithms
Data Structures & Algorithms
eBooks
eBooks
Electrical & Electronics Engineering
Electrical & Electronics Engineering
English (School)
English (School)
General Aptitude
General Aptitude
General Knowledge
General Knowledge
General Knowledge & Current Affairs
General Knowledge & Current Affairs
Languages & Literature
Languages & Literature
Law & Legal Studies
Law & Legal Studies
Major Competitive Exams
Major Competitive Exams
Mathematics (School)
Mathematics (School)
Mechanical Engineering
Mechanical Engineering
Medical Science
Medical Science
Physics (School & Undergraduate)
Physics (School & Undergraduate)
Quantitative Aptitude & Reasoning
Quantitative Aptitude & Reasoning
Social Science (School)
Social Science (School)
Technical
Technical
Verbal and Reasoning
Verbal and Reasoning
Vocational & Skill Development
Vocational & Skill Development
Soulshift Feedback ×

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?

Not likely Very likely