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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^{2x + \log x}}} dx = $
  • ✓
    $\frac{1}{4}(2x - 1){e^{2x}} + c$
  • B
    $\frac{1}{4}(2x+ 1){e^{2x}} + c$
  • C
    $\frac{1}{2}(2x - 1){e^{2x}} + c$
  • D
    $\frac{1}{2}(2x + 1){e^{2x}} + c$
✓

Answer

Correct option: A.
$\frac{1}{4}(2x - 1){e^{2x}} + c$
a
(a)$\int_{}^{} {{e^{2x + \log x}}dx} = \int_{}^{} {x{e^{2x}}dx} $
$ = \frac{{x{e^{2x}}}}{2} - \int_{}^{} {\frac{1}{2}{e^{2x}}dx + c} = \frac{{{e^{2x}}}}{4}(2x - 1) + c.$

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