Question

Encontre a integral indefinida dada por ∫x^2/(x^3+8)dx


A) 1/3∗ln∣x3∣+C

B) 1/3∗ln∣x3+8∣+C

C) −(1/2)∗ln∣x3−8∣+C

D) 1/4∗ln∣x5+8∣+C

E) ln∣x3+8∣+C

Answer 1

$\displaystyle \sf \int\left[\frac{x^2}{x^3+8}\right]dx \\\\\\ Fa{\c c}amos} : \\\\ x^3+8 = u \to 3x^2dx=du \\\\ Da{\'i}}: \\\\ \frac{1}{3}\int \left[\frac{3x^2}{x^3+8}\right]dx \\\\\\ \frac{1}{3}\int \frac{du}{u} = \frac{1}{3}\cdot \ln|u|+C \\\\\\ \huge\boxed{\sf \frac{1}{3}\cdot \ln|x^3+8|+C }\checkmark$

item B