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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{{x - 2}}{{{x^2} - 4x + 3}}dx = } $
  • ✓
    $\log \sqrt {{x^2} - 4x + 3} + c$
  • B
    $x\log (x - 3) - 2\log (x - 2) + c$
  • C
    $\log [(x - 3)(x - 1)]$
  • D
    None of these
✓

Answer

Correct option: A.
$\log \sqrt {{x^2} - 4x + 3} + c$
a
(a) Put ${x^2} - 4x + 3 = t \Rightarrow (2x - 4)\,dx = dt$
$ \Rightarrow (x - 2)\,dx = \frac{1}{2}dt,$ then it reduces to
$\frac{1}{2}\int_{}^{} {\frac{{dt}}{t} = \frac{1}{2}\log t + c = \frac{1}{2}\log ({x^2} - 4x + 3) + c.} $

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