∫ cos ( t ) t d t = 2 ∫ c o s u d u = 2 3 u 2 / 3 + c = {\displaystyle \int {\frac {\cos {({\sqrt {t}})}}{\sqrt {t}}}dt=2\int cosudu={\frac {2}{3}}u^{2/3}+c=}
u = u d u = 1 2 1 t d x 2 d u = 1 t d x {\displaystyle {\begin{aligned}u&={\sqrt {u}}\\[2ex]du&={\frac {1}{2}}\ {\frac {1}{\sqrt {t}}}dx\\[2ex]2du&={\frac {1}{\sqrt {t}}}dx\end{aligned}}}
![{\displaystyle {\begin{aligned}u&={\sqrt {u}}\\[2ex]du&={\frac {1}{2}}\ {\frac {1}{\sqrt {t}}}dx\\[2ex]2du&={\frac {1}{\sqrt {t}}}dx\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/3a37f2379e73449da9a402a6551cdea68c52b387)