5.3 The Fundamental Theorem of Calculus/15

$y=\int _{0}^{tan(x)}{\sqrt {t+{\sqrt {t}}}}\,dt$

${\begin{aligned}{\frac {d}{dx}}(y)=\int _{0}^{tan(x)}{\sqrt {t+{\sqrt {t}}}}\,dt\,=\sec ^{2}(x)\cdot {\sqrt {tan(x)+{\sqrt {t}}an(x)}})-0\cdot {\sqrt {0+{\sqrt {0}}}}\,=\sec ^{2}(x)\cdot {\sqrt {tan(x)+{\sqrt {t}}an(x)}})\end{aligned}}$

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