Determine as primitivas das funções:
a) ![x^{5/3} x^{5/3}](https://tex.z-dn.net/?f=+x%5E%7B5%2F3%7D+)
b) ![x^{-1/3} x^{-1/3}](https://tex.z-dn.net/?f=+x%5E%7B-1%2F3%7D+)
c) ![\frac{1}{ x^{2} } \frac{1}{ x^{2} }](https://tex.z-dn.net/?f=+%5Cfrac%7B1%7D%7B+x%5E%7B2%7D+%7D+)
d) ![\frac{1}{ \sqrt{x} } \frac{1}{ \sqrt{x} }](https://tex.z-dn.net/?f=+%5Cfrac%7B1%7D%7B+%5Csqrt%7Bx%7D+%7D+)
Soluções para a tarefa
Respondido por
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{5}{3}} dx = \frac{3x^{\frac{8}{3}}}{8}+C](https://tex.z-dn.net/?f=%5Cint+x%5E%7B%5Cfrac%7B5%7D%7B3%7D%7D+dx+%3D+%5Cfrac%7B3x%5E%7B%5Cfrac%7B8%7D%7B3%7D%7D%7D%7B8%7D%2BC)
![\int x^{-\frac{1}{3}}=\frac{3x^{\frac{2}{3}}}{2}+C \int x^{-\frac{1}{3}}=\frac{3x^{\frac{2}{3}}}{2}+C](https://tex.z-dn.net/?f=%5Cint+x%5E%7B-%5Cfrac%7B1%7D%7B3%7D%7D%3D%5Cfrac%7B3x%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%7D%7B2%7D%2BC)
![\int \frac{1}{x^2} dx=-\frac{1}{x}+C \int \frac{1}{x^2} dx=-\frac{1}{x}+C](https://tex.z-dn.net/?f=%5Cint+%5Cfrac%7B1%7D%7Bx%5E2%7D+dx%3D-%5Cfrac%7B1%7D%7Bx%7D%2BC)
![\int \frac{1}{x^2} dx = 2 \sqrt{x} +C \int \frac{1}{x^2} dx = 2 \sqrt{x} +C](https://tex.z-dn.net/?f=%5Cint+%5Cfrac%7B1%7D%7Bx%5E2%7D+dx+%3D+2+%5Csqrt%7Bx%7D+%2BC)
Perguntas interessantes