Question

Calcule a integral indefinida:

formula

Answer 1

$\int\limits { \sqrt[3]{x^2} + \frac{1}{3x} } \, dx$

reescrevendo
$\int\limits {x^{ \frac{2}{3}}+ \frac{1}{3} *(x)^{-1} }} \, dx = \frac{x^{ \frac{2}{3}+1 }}{ \frac{2}{3}+1 }+ \frac{1}{3} * ln(x) = \frac{x^{ \frac{5}{3} }}{ \frac{5}{3} }+ \frac{ln(x)}{3} }$

$= \frac{3x^{ \frac{5}{3} }}{5} + \frac{ln(x)}{3} } = \boxed{\boxed{ \frac{3 \sqrt[3]{x^5} }{5} + \frac{ln(x)}{3} +C}}$