Question

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

Answer 1

$$\int \frac{\sin \sqrt{x}}{\sqrt{x}}dx$$
$$\text{Let}\sqrt{x}=t$$
$$\Rightarrow \frac{1}{2\sqrt{x}}=\frac{dt}{dx}$$
$$\Rightarrow \frac{dx}{\sqrt{x}}=2dt$$
$$Now,\int \frac{\sin \sqrt{x}}{\sqrt{x}}dx$$
$$=2\int \text{sin t dt}$$
$$=2[-\cos t]+C$$
$$=-2\cos \sqrt{x}+C$$