∫ x ⋅ s i n ( x 2 ) d x ∫ s i n ( t ) 2 d t 1 2 ⋅ ∫ s i n ( t ) d t 1 2 ⋅ ( c o s ( x 2 ) ) = − c o s ( x 2 ) 2 + C {\displaystyle {\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}}+C\end{aligned}}}
![{\displaystyle {\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}}+C\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/c09670cea3245f8de8d60fcdc5e82846cbb261ac)