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7.1 inderfinite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.1 inderfinite integral1 Mark
MCQ
The value of $\int_{}^{} {\frac{{{e^x}}}{{{e^x} + 1}}} \,dx$ is
  • A
    ${e^x} + c$
  • B
    $({e^x} + 1) + c$
  • ✓
    $\log ({e^x} + 1) + c$
  • D
    None of these
✓

Answer

Correct option: C.
$\log ({e^x} + 1) + c$
c
(c) Put ${e^x} + 1 = t \Rightarrow {e^x}dx = dt$
$\therefore $ $\int_{}^{} {\frac{{{e^x}}}{{{e^x} + 1}}dx = \int_{}^{} {\frac{{dt}}{t} = \log t + c = \log ({e^x} + 1) + c} } $.

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