Concursul "Nicolae Coculescu" 2009, problema 2
Posted: Sat Nov 28, 2009 8:40 am
Sa se calculeze \( \int \frac{x}{\sqrt{x}+\sqrt{1-x}},x\in(0,1) \).
Florian Dumitrel
Florian Dumitrel
\( \mbox{Facand substitutia: }x=\sin^2y;\ y \in\left(0;\frac{\pi}{2}\right) \mbox{, integrala se reduce la: }2.\int{\frac{\sin^3y.\cos y .dy}{\sin y+\cos y}};\\
\mbox{iar aceasta integrala cu substitutia: }tg {\frac{y}{2}}=t;\ t\in\left(0;\frac{\pi}{2}\right)\mbox{, se reduce la integrala unei functii rationale.}
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