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Find the integral ∫ (x^2 - 1)/(x - 1) dx.
Find the integral ∫ (x^2 - 1)/(x - 1) dx.
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Practice Questions
1 question
Q1
Find the integral ∫ (x^2 - 1)/(x - 1) dx.
(1/3)x^3 - x + C
(1/3)x^3 - x - 1 + C
(1/3)x^3 - x + 1
(1/3)x^3 - x - 1
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The integrand simplifies to x + 1. Therefore, ∫ (x + 1) dx = (1/2)x^2 + x + C.
Questions & Step-by-step Solutions
1 item
Q
Q: Find the integral ∫ (x^2 - 1)/(x - 1) dx.
Solution:
The integrand simplifies to x + 1. Therefore, ∫ (x + 1) dx = (1/2)x^2 + x + C.
Steps: 8
Show Steps
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.
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