Answer
$-2cos(\sqrt x) +C$
Work Step by Step
Evaluate the Integral using substitution: $\int \frac{sin\sqrt x}{\sqrt x}$
Substitution Rule: $\int f(g(x))g’(x)dx = \int f(u)du$
$u= \sqrt x$
$du =\frac{1}{2\sqrt x}$
Since $du$ in the expression is equal to $\frac{1}{\sqrt x}$ it must be multiplied by $2$
Solve the integral in terms of $u$:
$\int sin(u)(2)du$
$-2cos(u) +C $
Substitute for $u$:
$-2cos(\sqrt x) +C$
