∫1-3 (x^2016+x^2014)/x^2015 dx
(x^2016+x^2014)/x^2015=
x^2014(x^2 + 1)/x^2015 Stim ca x^a/x^b= 1/(x^(b-a))
x^2014/x^2015=1/x^(2015-2014)=1/x
x^2014(x^2 + 1)/x^2015= (x^2+1)/x= x^2/x + 1/x= x+1/x
∫(x+1/x) dx= ln(|x|)+x^2/2+C
∫1-3(ln(|x|)+x^2/2+C)dx=
lim x→3 (ln(|x|)+x^2/2+C) - lim x→1 (ln(|x|)+x^2/2+C)=
9/2 + ln(3) - 1/2 - 1/2 - ln(1)= Stim ca ln1=0
9/2 + ln(3) - 1/2 - 1/2=
4 + ln(3)
