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Black Advanced Problems in Mathematics
Exam
Black Advanced Problems in Mathematics
Subject
Mathematics
Chapter
Indefinite and Definite Integration

Black Advanced Problems in Mathematics · Mathematics · Indefinite and Definite Integration

Evaluate : ∫ (x^3 + 3x^2 + x + 9)/((x^2 + 1)(x^2 + 3)) dx .

Evaluate : ∫x3+3x2+x+9(x2+1)(x2+3)dx\int \frac{x^3 + 3x^2 + x + 9}{(x^2 + 1)(x^2 + 3)} dx.

Options

  1. Aln⁡∣x2+3∣+3tan⁡−1x+c\ln |x^2 + 3| + 3 \tan^{-1} x + c
  2. B12ln⁡∣x2+3∣+tan⁡−1x+c\frac{1}{2} \ln |x^2 + 3| + \tan^{-1} x + c
  3. C12ln⁡∣x2+3∣+3tan⁡−1x+c\frac{1}{2} \ln |x^2 + 3| + 3 \tan^{-1} x + c
  4. Dln⁡∣x2+3∣−tan⁡−1x+c\ln |x^2 + 3| - \tan^{-1} x + c

Correct answer

C. 12ln⁡∣x2+3∣+3tan⁡−1x+c\frac{1}{2} \ln |x^2 + 3| + 3 \tan^{-1} x + c

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