Question

Alguém pode me ajudar a resolver essa integral?

Answer 1

Resposta:

(x+2)³=x³+6x²+12x+2³

(x+2)³=x³+6x²+12x+8

(x+2)³=x³+8+6x²+12x

(x+2)³=x³+8+6x*(x+2)

x³+8=(x+2)³-6x*(x+2)

x³+8=(x+2)*[(x+2)²-6x]

x³+8=(x+2)*[x²+4x+4-6x]

x³+8=(x+2)*[x²-2x+4]

∫ (x³+8)/(x+2)  dx

∫ (x+2)*[x²-2x+4]/(x+2)  dx

∫ x²-2x+4  dx

=x³/3 -2x²/2+4x + c

f(x)=x³/3 -x² + 4x + const.

f(1)=1/3-1+4 + constante