A) \[\sin \sqrt{x}+c\]
B) \[2\sin \sqrt{x}+c\]
C) \[-\sin \sqrt{x}+c\]
D) \[-2\sin \sqrt{x}+c\]
Correct Answer: B
Solution :
Let \[I=\int{\frac{\cos \sqrt{x}}{\sqrt{x}}}dx\] Let \[\sqrt{x}=t\] \[\Rightarrow \] \[\frac{1}{2\sqrt{x}}dx=dt\] \[\Rightarrow \] \[\frac{1}{\sqrt{x}}dx=2dt\] \[\therefore \] \[I=\int{\cos t2.dt}\] \[=2\sin t+c\] \[=2\sin \sqrt{x}+c\]
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