Question

Me ajuda a calcular a integral PORFAVOOOR de
∫ln (x+2)/(x+2).dx

Answer 1

(x+2) = w
dw = dx
∫ln (x+2)/(x+2).dx = ∫lnw/w dw
Temos que:
∫udv = uv - ∫vdu
fazendo com que:
dv = 1/w ⇒ v= lnw; u = lnw ⇒ du= 1/w
Temos que:
∫lnw/w dw = (lnw)² - ∫lnw . 1/w
2∫lnw/w dw = (lnw)²
∫lnw/w dw = 1/2 (lnw)² + C