∫ { x s i n ( x 2 ) d x {\displaystyle \int \{xsin{(x^{2})}dx}
u = x 2 d u = 2 x d x 1 2 d u = d x {\displaystyle {\begin{aligned}u&=x^{2}\\[2ex]du&=2xdx\\[2ex]{\frac {1}{2}}du&=dx\\[2ex]\end{aligned}}}
∫ { x s i n ( x 2 ) d x = 1 2 ∫ sin u d u = − 1 2 c o s u + C = − 1 2 c o s x 2 + C {\displaystyle {\begin{aligned}\int \{xsin{(x^{2})}dx&={\frac {1}{2}}\int \sin {u}du\\[2ex]&=-{\frac {1}{2}}cos{u}+C&=-{\frac {1}{2}}cos{x^{2}}+C\end{aligned}}}
![{\displaystyle {\begin{aligned}u&=x^{2}\\[2ex]du&=2xdx\\[2ex]{\frac {1}{2}}du&=dx\\[2ex]\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/d3662e4ad2b3d50be2a69669e39b54ac46042ca4)
![{\displaystyle {\begin{aligned}\int \{xsin{(x^{2})}dx&={\frac {1}{2}}\int \sin {u}du\\[2ex]&=-{\frac {1}{2}}cos{u}+C&=-{\frac {1}{2}}cos{x^{2}}+C\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/ba672db32537e9fd248ff268d2c8a2ad0217d92b)