∫ cos ( t ) t d t {\displaystyle \int {\frac {\cos {({\sqrt {t}})}}{\sqrt {t}}}dt}
u = t d u = 1 2 1 t d x 2 d u = 1 t d x {\displaystyle {\begin{aligned}u&={\sqrt {t}}\\[2ex]du&={\frac {1}{2}}\ {\frac {1}{\sqrt {t}}}dx\\[2ex]2du&={\frac {1}{\sqrt {t}}}dx\end{aligned}}}
∫ cos ( t ) t d t = 2 ∫ cos u d u = 2 sin u + c = 2 sin ( t ) + c {\displaystyle {\begin{aligned}\int {\frac {\cos {({\sqrt {t}})}}{\sqrt {t}}}dt&=2\int \cos {u}du\\[2ex]&=2\sin {u}+c\\[2ex]&=2\sin({\sqrt {t}})+c\\[2ex]\end{aligned}}}
![{\displaystyle {\begin{aligned}u&={\sqrt {t}}\\[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/70fed9f73de597a61b5eb92fde65a887a6e2dffe)
![{\displaystyle {\begin{aligned}\int {\frac {\cos {({\sqrt {t}})}}{\sqrt {t}}}dt&=2\int \cos {u}du\\[2ex]&=2\sin {u}+c\\[2ex]&=2\sin({\sqrt {t}})+c\\[2ex]\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/7e668025b4d0cbe98ca2149ab5b23912a0a8bfd5)