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STD 12 - 7.1 inderfinite integral — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 7.1 inderfinite integral4 Marks
MCQ
$\int_{}^{} {{e^x}\left( {\frac{1}{x} - \frac{1}{{{x^2}}}} \right)} \,dx = $
  • A
    $ - \frac{{{e^x}}}{{{x^2}}} + c$
  • B
    $\frac{{{e^x}}}{{{x^2}}} + c$
  • ✓
    $\frac{{{e^x}}}{x} + c$
  • D
    $ - \frac{{{e^x}}}{x} + c$
✓

Answer

Correct option: C.
$\frac{{{e^x}}}{x} + c$
c
(c)$\int_{}^{} {{e^x}\left( {\frac{1}{x} - \frac{1}{{{x^2}}}} \right)} \,dx = {e^x}\frac{1}{x} + c$
Since, we have $\int_{}^{} {{e^x}\left\{ {f(x) + f'(x)} \right\}\,dx} = {e^x}f(x) + c.$

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