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całka wymierna
: 11 lut 2009, o 06:03
autor: zizu_56
Oblicz
\(\displaystyle{ \int \frac{x ^{2}+13}{x ^{2}+4x+13 }}\)
całka wymierna
: 11 lut 2009, o 08:43
autor: pepis
\(\displaystyle{ \int \frac{x ^{2}+13+4x-4x}{x ^{2}+4x+13 }dx=\int dx -2\int\frac{2x+4-4}{x ^{2}+4x+13 }dx=\int dx -2\int\frac{2x+4}{x ^{2}+4x+13 }dx+ 8\int\frac{1}{(x+2)^{2}+9 }dx= x-2ln|x ^{2}+4x+13|+ \frac{8}{3}arctg( \frac{x+2}{3} )+C}\)