e^ x x dx = - Vidyadip

MCQ

$\int {\frac{{{e^{\sqrt x }}}}{{\sqrt x }}dx} = $

A
${e^{\sqrt x }}$
B
$\frac{{{e^{\sqrt x }}}}{2}$
✓
$2\,{e^{\sqrt x }}$
D
$\sqrt x \,.\,{e^{\sqrt x }}$

✓

Answer

Correct option: C.

$2\,{e^{\sqrt x }}$

c
(c) $I = \int {\frac{{{e^{\sqrt x }}}}{{\sqrt x }}dx\,}$

Put $\sqrt x = t$, $\therefore \frac{1}{{2\sqrt x }}dx = dt$

$I = 2\int {{e^t}dt = 2{e^t} + C = 2{e^{\sqrt x }} + C} $.

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