Integrals · Class 12 · CBSE · Science Mathematics

Evaluate ∫₀¹ x ln(1 + x²) dx.

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

hard · MCQ · Q-44BCC1

Evaluate ∫₀¹ x ln(1 + x²) dx.

  1. A.ln 2 − 1/2Correct answer
  2. B.ln 2 + 1/2
  3. C.1/2 − ln 2
  4. D.ln 2

Solution

Put u=1+x2u=1+x^2, so du=2x dxdu=2x\,dx. Then the integral is 12∫12ln⁡u du=12[uln⁡u−u]12=ln⁡2−12\frac12\int_1^2\ln u\,du=\frac12[u\ln u-u]_1^2=\ln2-\frac12.

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