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Integrals · Class 12 · CBSE · Science Mathematics

Evaluate ∫ x/(x² + 1) dx.

Practice question from Integrals (Class 12 · CBSE · Science Mathematics), with the correct answer and a step-by-step solution.

easy · MCQ · Q-3692FB

Evaluate ∫ x/(x² + 1) dx.

  1. A.ln(x² + 1) + C
  2. B.(1/2)ln(x² + 1) + CCorrect answer
  3. C.1/(x² + 1) + C
  4. D.tan⁻¹x + C

Solution

Let u=x2+1u=x^2+1, so du=2x dxdu=2x\,dx. Therefore, ∫xx2+1 dx=12∫duu=12ln⁡(x2+1)+C\int \frac{x}{x^2+1}\,dx=\frac12\int\frac{du}{u}=\frac12\ln(x^2+1)+C.

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