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What is the integral of x^n where n ≠ -1? (2021)

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Question: What is the integral of x^n where n ≠ -1? (2021)

Options:

  1. (1/n)x^(n+1) + C
  2. (1/(n+1))x^n + C
  3. (1/(n+1))x^(n+1) + C
  4. nx^(n-1) + C

Correct Answer: (1/(n+1))x^(n+1) + C

Exam Year: 2021

Solution: 

The integral of x^n is (1/(n+1))x^(n+1) + C, provided n ≠ -1.

What is the integral of x^n where n ≠ -1? (2021)

Practice Questions

Q1
What is the integral of x^n where n ≠ -1? (2021)
  1. (1/n)x^(n+1) + C
  2. (1/(n+1))x^n + C
  3. (1/(n+1))x^(n+1) + C
  4. nx^(n-1) + C

Questions & Step-by-Step Solutions

What is the integral of x^n where n ≠ -1? (2021)
  • Step 1: Identify the function you want to integrate, which is x^n.
  • Step 2: Recognize that n is a constant and it is not equal to -1.
  • Step 3: Use the power rule for integration, which states that the integral of x^n is (1/(n+1))x^(n+1).
  • Step 4: Add the constant of integration, C, to the result to account for all possible antiderivatives.
  • Step 5: Write the final answer as (1/(n+1))x^(n+1) + C.
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