Question

$\int \frac{\cos \sqrt{x}}{\sqrt{x}}dx=$

• A. $2\sin \sqrt{x}+c$
• B. ${\sin }^2\sqrt{x}+c$
• C. ${\cos }^2\sqrt{x}+c$
• D. $2\cos \sqrt{x}+c$

Answer 1

The correct option is A $2\sin \sqrt{x}+c$

Substitute$\sqrt{x}=t$

$\Rightarrow \frac{1}{2}\frac{1}{\sqrt{x}}dx=dt\Rightarrow \frac{1}{\sqrt{x}}dx=2dt$

$\int \cos t\cdot 2dt=2\int \cos tdt$

$=2\sin t+c$

$=2\sin \sqrt{x}+c$

$\int \frac{cos\sqrt{x}}{\sqrt{2}}dx=2sin\sqrt{x}+c$