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7.1 inderfinite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.1 inderfinite integral1 Mark
MCQ
$\int_{}^{} {\frac{{f'(x)}}{{{{[f(x)]}^2}}}} \;dx = $
  • ✓
    $ - {[f(x)]^{ - 1}} + c$
  • B
    $\log [f(x)] + c$
  • C
    ${e^{f(x)}} + c$
  • D
    None of these
✓

Answer

Correct option: A.
$ - {[f(x)]^{ - 1}} + c$
a
(a) Put $f(x) = t \Rightarrow f'(x)\,dx = dt,$ then
$\int_{}^{} {\frac{{f'(x)}}{{|f(x){|^2}}}\,dx} = \int_{}^{} {\frac{1}{{{t^2}}}\,dt} = - \frac{1}{t} + c = - \frac{1}{{f(x)}} + c.$

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