Разложить функцию по степеням икс

f (x) =

F (x) = 3/5ln (x²+6x+5)

x²+6x+5=0

x1+x2=-6 U x1*x2=5⇒x1=-5 U x2=-1

f (x) = 3/5ln[ (x+1) (x+5) ]=3/5ln (x+1) + 3/5ln (x+5)

1) f1 (x) = ln (x+1) = x-x²/2+x³/3-x^4/4 + ... + (-1) ^n*x^n/n

2) f2 (x) = ln (x+5) = ln[5 (1+x/5) ]=ln5+ln (1+x/5) =

=ln5+x/5-x²/2*5²+x³/3*5^3-x^4/4*5^4 + ... + (-1) ^n*x^n/n*5^n

f (x) = 3/5*[x-x²/2+x³/3-x^4/4 + ... + (-1) ^n*x^n/n + ln5+x/5-x²/2*5²+x³/3*5^3-x^4/4*5^4 + ... + (-1) ^n*x^n/n*5^n) = 3/5 * (ln5+6x/5-26x²/50+126x^3/375-

-626x^4/22500 + ... + (-1) ^n*[ (5^n*+1) * x^n) ] / (n*5^n) ]