Answer
$cos(1/x) + C$
Work Step by Step
$u = 1/x$ determine u
$du = -1/x^2 dx$ derive
$\int1/x^2 sin(1/x)dx$ restate problem
$-\int sin(1/x)(-1/x^2)dx$ rewrite problem
$-\int sin(u) du$ substitute $1/x$ for $u$, $-1/x^2$ for $du$.
$-(-cos(u)) + C$ integral of sine equals negative cosine plus a constant
$cos(u) + C$ simplify
$cos(1/x) + C$ substitute $u$ for %1/x%.
