5.5 The Substitution Rule/7

${\begin{aligned}&\int {x\cdot sin{(x^{2})}}dx\\[2ex]&\int {\cfrac {sin(t)}{2}}dt\\[2ex]&{\cfrac {1}{2}}\cdot \int {sin(t)}dt\\[2ex]&{\cfrac {1}{2}}\cdot (cos(x^{2}))\\[2ex]&-{\cfrac {cos(x^{2})}{2}}\end{aligned}}$