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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

∫ (x + 2) dx (x^2 + 3x + 3) x + 1 is equal to : *(where C is...

∫(x+2)dx(x2+3x+3)x+1\int \frac{(x + 2) dx}{(x^2 + 3x + 3)\sqrt{x + 1}} is equal to : *(where C is arbitrary constant.)*

Options

  1. A23tan⁡−1(x3(x+1))+C\frac{2}{\sqrt{3}} \tan^{-1} \left( \frac{x}{\sqrt{3(x+1)}} \right) + C
  2. B23tan⁡−1(x3(x+1))+C\frac{2}{\sqrt{3}} \tan^{-1} \left( \frac{\sqrt{x}}{\sqrt{3(x+1)}} \right) + C
  3. C13tan⁡−1(x3(x+1))+C\frac{1}{\sqrt{3}} \tan^{-1} \left( \frac{\sqrt{x}}{3(x+1)} \right) + C
  4. D23tan⁡−1(x3(x+1))+C\frac{2}{\sqrt{3}} \tan^{-1} \left( \frac{x}{\sqrt{3}(x+1)} \right) + C

Correct answer

A. 23tan⁡−1(x3(x+1))+C\frac{2}{\sqrt{3}} \tan^{-1} \left( \frac{x}{\sqrt{3(x+1)}} \right) + C

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