Răspuns:
9^log₃(2x+3)=
3^2log₃(2x+3)=
3^log₃(2x+3)²=
(2x+3)²
I=∫(2x+3)²dx=
2x+3=y
Schimbi limitele de integrare
x=1
y=2*1+3=2+3=5
x=2
2x+3=y
y=2*2+3=4+3=7
2dx=dy
dx=dy/2
I=1/2∫y²dy=1/2 y³/3=y³/6=(7³/6-5³/6)=(343-125)/6 revin
Sa retii formula
x^logₓa=a
o)Logaritmul natural are baza e deci
e^ln(6x²+4x+1)=6x²+4x+1
I=∫(6x²+4x+1)dx=
6∫x²dx+4∫dx+∫dx=
6*x³/3+4x²/2+x=
(2x³+2x²+x)║₀¹=
2*1³+2*1²+1)-(2*0³+2*0²+0)=
2+2+1=5-0=5
Explicație pas cu pas:
