Calculus 8th Edition

$\int \frac{cos(lnt)}{t}dt=sin(lnt)+Constant$
Evaluate $\int \frac{cos(lnt)}{t}dt$. Consider $ln t =u$ and $\frac{1}{t} dt = du$ Thus, $\int \frac{cos(lnt)}{t}dt=\int cos (u) du$ $=sin(u)+ Constant$ $=sin(lnt)+Constant$ Hence, $\int \frac{cos(lnt)}{t}dt=sin(lnt)+Constant$