Całka z podstawieniem uniwersalnym
: 10 cze 2010, o 22:55
Proszę o skorygowanie ewentualnych błędów:
\(\displaystyle{ \int_{}^{} \frac{dx}{4+2cosx}dt = \int_{}^{} \frac{ \frac{2}{1+ t^{2} } }{4+2( \frac{1- t^{2} }{1+ t^{2} } )}dt= \int_{}^{} \frac{ \frac{2}{1+ t^{2} } }{ \frac{6+ t^{2} }{2+t^{2}} }dt= \int_{}^{} \frac{2}{1+t^{2}} \cdot \frac{1+t^{2}}{3+t^{2} }dt}\)
\(\displaystyle{ \int_{}^{} \frac{dx}{4+2cosx}dt = \int_{}^{} \frac{ \frac{2}{1+ t^{2} } }{4+2( \frac{1- t^{2} }{1+ t^{2} } )}dt= \int_{}^{} \frac{ \frac{2}{1+ t^{2} } }{ \frac{6+ t^{2} }{2+t^{2}} }dt= \int_{}^{} \frac{2}{1+t^{2}} \cdot \frac{1+t^{2}}{3+t^{2} }dt}\)