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7.1 inderfinite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.1 inderfinite integral1 Mark
MCQ
$\int_{}^{} {{e^x}[\tan x - \log (\cos x)]\;dx = } $
  • ✓
    ${e^x}\log (\sec x) + c$
  • B
    ${e^x}\log (\cos {\rm{ec}}x) + c$
  • C
    ${e^x}\log (\cos x) + c$
  • D
    ${e^x}\log (\sin x) + c$
✓

Answer

Correct option: A.
${e^x}\log (\sec x) + c$
a
(a)$\int_{}^{} {{e^x}[\tan x - \log (\cos x)]\,dx} = \int_{}^{} {{e^x}[\tan x + \log (\sec x)]} \,dx$
$ = {e^x}\log (\sec x) + c$
$\left\{ {{\rm{Since}}\int_{}^{} {{e^x}\left\{ {f(x) + f'(x)} \right\}dx = {e^x}f(x) + c} } \right\}$.

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