Question

Determine as primitivas das funções:

a) $x^{5/3}$

b) $x^{-1/3}$

c) $\frac{1}{ x^{2} }$

d) $\frac{1}{ \sqrt{x} }$

Answer 1

Utilizando as regras das integrais imediatas, podemos escrever:

$\int x^{\frac{5}{3}} dx = \frac{3x^{\frac{8}{3}}}{8}+C$

$\int x^{-\frac{1}{3}}=\frac{3x^{\frac{2}{3}}}{2}+C$

$\int \frac{1}{x^2} dx=-\frac{1}{x}+C$

$\int \frac{1}{x^2} dx = 2 \sqrt{x} +C$