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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
The value of $\int {\frac{1}{{{{(x - 5)}^2}}}\,\,dx} $ is
  • A
    $\frac{1}{{x - 5}} + c$
  • ✓
    $ - \frac{1}{{x - 5}} + c$
  • C
    $\frac{2}{{{{\left( {x - 5} \right)}^3}}} + c$
  • D
    $ - 2{\left( {x - 5} \right)^3} + c$
✓

Answer

Correct option: B.
$ - \frac{1}{{x - 5}} + c$
b
(b)$I = \int {\frac{1}{{{{(x - 5)}^2}}}dx} $$ = \frac{{{{(x - 5)}^{ - 2 + 1}}}}{{ - 2 + 1}} + c = \frac{{{{(x - 5)}^{ - 1}}}}{{ - 1}} + c$
$ = - \frac{1}{{(x - 5)}} + c$.

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