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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}}{{{e^x} - 1}} = } $
  • ✓
    $\ln (1 - {e^{ - x}}) + c$
  • B
    $ - \ln (1 - {e^{ - x}}) + c$
  • C
    $\ln ({e^x} - 1) + c$
  • D
    None of these
✓

Answer

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

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