Предел.[tex] \int\limits \sqrt{2-sin*3x} *cos3x*dx ^_ {} \, [/tex]. Created by 43233. matematika-ru

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Предел.[tex] \int\limits \sqrt{2-sin*3x} *cos3x*dx ^_ {} \, [/tex]

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$\int \sqrt{2-sin3x}\cdot cos3x\, dx=[\, t=2-sin3x,\; dt=-3cos3x\, dx\, ]=\\\\=-\frac{1}{3}\cdot \int \sqrt{t}\cdot dt=-\frac{1}{3}\cdot \frac{t^{\frac{3}{2}}}{\frac{3}{2}}+C=-\frac{2}{9}\cdot \sqrt{(2-sin3x)^3}+C$

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