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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_{}^{} {\frac{{{e^x}dx}}{{\sqrt {a + b{e^x}} }}} = $
  • ✓
    $2/b\sqrt {a + b{e^x}} + c$
  • B
    $2b\sqrt {a + b{e^x}} + c$
  • C
    $\frac{1}{{2b}}\sqrt {a + b{e^x}} $
  • D
    $\frac{a}{b}\sqrt {a + b{e^x}} + c$
✓

Answer

Correct option: A.
$2/b\sqrt {a + b{e^x}} + c$
a
(a) Put $a + b{e^x} = t \Rightarrow b{e^x}dx = dt,$ then
$\int_{}^{} {\frac{{{e^x}dx}}{{\sqrt {a + b{e^x}} }}\, = \frac{1}{b}\int_{}^{} {\frac{1}{{\sqrt t }}\,dt = \frac{2}{b}\sqrt t + c} } $$ = \frac{{2\sqrt {a + b{e^x}} }}{b} + c.$

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