Интегралы .Номера 3.20, 3.21, 3,22, 3,23,3.4. Created by antonner. algebra-ru

Интегралы .Номера 3.20, 3.21, 3,22, 3,23,3.4...

MAXIS95 $3.20) \int\limits { \frac{lnx}{ \sqrt{x} } } \, dx =|u=lnx||dv= \frac{1}{ \sqrt{x} } dx||du= \frac{dx}{x}||v=2 \sqrt{x} |=2 \sqrt{x} *lnx \\ - 2\int\limits{ x^{- \frac{1}{2} } } \, dx=2 \sqrt{x} *lnx-4 \sqrt{x} +C \\ 3.21) \int\limits {(2x-3)sin\frac{x}{2} } \, dx =|u=2x-3||dv=sin \frac{x}{2}dx||du=2| \\ |v=-2cos \frac{x}{2} |=(2x-3)*(-2cos \frac{x}{2})+4 \int\limits {cos \frac{x}{2} } \, dx = \\ =(2x-3)*(-2cos \frac{x}{2})+8sin \frac{x}{2}+C$

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