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CA Foundation · Quantitative Aptitude · Differential and Integral Calculus

Evaluate ∫ (x + 1)² / x dx, for x > 0, where C is the constant of integration.

The answer is x²/2 + 2x + log x + C. Expanding the numerator and dividing by x gives x + 2 + 1/x, and integrating each term gives x²/2, 2x and log x respectively. The power rule cannot be used for 1/x.

  1. Ax²/2 + 2x + log x + CCorrect
  2. Bx²/2 + 2x − 1/x + C
  3. C(x + 1)³/(3x) + C
  4. Dx² + 2x + log x + C

Explanation

Expand: (x² + 2x + 1)/x = x + 2 + 1/x. Integrating gives x²/2 + 2x + log x + C. The option with −1/x treats 1/x as x^(−1) using the power rule, which fails for n = −1, where the result is log x.

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