A) \[{{e}^{\sqrt{x}}}\]
B) \[\frac{{{e}^{\sqrt{x}}}}{2}\]
C) \[2\,{{e}^{\sqrt{x}}}\]
D) \[\sqrt{x}\,.\,{{e}^{\sqrt{x}}}\]
Correct Answer: C
Solution :
\[I=\int{\frac{{{e}^{\sqrt{x}}}}{\sqrt{x}}dx.\,}\]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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