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STD 12 - 7.1 inderfinite integral — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 7.1 inderfinite integral1 Mark
MCQ
$\int_{}^{} {\frac{{dx}}{{(x + 1)(x + 2)}} = } $
  • A
    $\log \frac{{x + 2}}{{x + 1}} + c$
  • B
    $\log (x + 1) + \log (x + 2) + c$
  • ✓
    $\log \frac{{x + 1}}{{x + 2}} + c$
  • D
    None of these
✓

Answer

Correct option: C.
$\log \frac{{x + 1}}{{x + 2}} + c$
c
(c)$\int_{}^{} {\frac{{dx}}{{(x + 1)(x + 2)}}} = \int_{}^{} {\left( {\frac{1}{{x + 1}} - \frac{1}{{x + 2}}} \right)} \,dx$
$ = \log (x + 1) - \log (x + 2) + c = \log \frac{{x + 1}}{{x + 2}} + c.$

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