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INTEGRALS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsINTEGRALS1 Mark
MCQ
Choose the correct answer in Exercise:
$\int\frac{\text{dx}}{\text{x}^2+2\text{x}+2}\text{equals}$
  • A
    $\text{x}\tan^{-1}(\text{x}+1)+\text{C}$
  • ✓
    $\tan^{-1}(\text{x}+1)+\text{C}$
  • C
    $(\text{x}+1)\tan^{-1}\text{x}+\text{C}$
  • D
    $\tan^{-1}\text{x}+\text{C}$
✓

Answer

Correct option: B.
$\tan^{-1}(\text{x}+1)+\text{C}$
$\int\frac{\text{dx}}{\text{x}^2+2\text{x}+2}$
$=\int\frac{1}{\text{x}^2+2\text{x}+1+1}\text{dx}$
$=\int\frac{1}{(\text{x+1})^2+(1)^2}\text{ dx}$
$=\tan^{-1}(\text{x}+1)+\text{C}$
Therefore, option (B) is correct.

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