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What is the value of the integral ∫(1/(x^2 + 1))dx?

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Question: What is the value of the integral ∫(1/(x^2 + 1))dx?

Options:

  1. tan^-1(x) + C
  2. sin^-1(x) + C
  3. cos^-1(x) + C
  4. ln(x) + C

Correct Answer: tan^-1(x) + C

Solution: 

The integral evaluates to tan^-1(x) + C.

What is the value of the integral ∫(1/(x^2 + 1))dx?

Practice Questions

Q1
What is the value of the integral ∫(1/(x^2 + 1))dx?
  1. tan^-1(x) + C
  2. sin^-1(x) + C
  3. cos^-1(x) + C
  4. ln(x) + C

Questions & Step-by-Step Solutions

What is the value of the integral ∫(1/(x^2 + 1))dx?
  • Step 1: Identify the integral we need to solve: ∫(1/(x^2 + 1))dx.
  • Step 2: Recognize that the integral of 1/(x^2 + 1) is a standard integral that equals arctan(x) or tan^-1(x).
  • Step 3: Write down the result of the integral: tan^-1(x) + C, where C is the constant of integration.
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