My Learning Cart
?
Categories
Account

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

₹0.0
Login to Download
  • 📥 Instant PDF Download
  • ♾ Lifetime Access
  • 🛡 Secure & Original Content

What’s inside this PDF?

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

Options:

  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

Correct Answer: (1/3)x^3 - x + C

Solution: 

The integrand simplifies to x + 1. Therefore, ∫ (x + 1) dx = (1/2)x^2 + x + C.

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.
Soulshift Feedback ×

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

Not likely Very likely
Home Practice Performance eBooks