Question

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

Answer 1

$$\begin{gathered} \int \frac{\cos \sqrt{x}}{\sqrt{x}}dx \\ \mathrm{Let}\sqrt{x}=t \\ \Rightarrow \frac{1}{2\sqrt{x}}=\frac{dt}{dx} \\ \Rightarrow \frac{dx}{\sqrt{x}}=2dt \\ \mathrm{Now},\int \frac{\cos \sqrt{x}}{\sqrt{x}}dx \\ =2\int \cos tdt \\ =2\sin t+C \\ =2\sin \sqrt{x}+C \end{gathered}$$