Question

O valor da integral indefinida abaixo, dx e de;

Answer 1

Boa tarde!

Solução!

$\displaystyle\int(3 x^{2} +x+ \frac{1}{ x^{3} })dx\\\\\\\\ \displaystyle\int(3 x^{2})dx+\displaystyle\int (x)dx+\displaystyle\int(\frac{1}{ x^{3} })dx\\\\\\\ I= \dfrac{3 x^{3} }{3}+ \frac{ x^{2} }{2} +\frac{ x^{-3+1} }{-3+1}\\\\\\\ I= x^{3} +\frac{ x^{2} }{2} +\frac{ x^{-2} }{-2}\\\\\\\ I= x^{3} +\frac{ x^{2} }{2} -\frac{ 1}{2 x^{2} }+c\\\\\\\\\\\\\\\\ \boxed{Resposta:I= x^{3} +\frac{ x^{2} }{2} -\frac{ 1}{2 x^{2} }+c~~Alternativa~~D}$

Boa tarde!
Bons estudos!

Answer 2

Olá, boa tarde ☺

Resolução:

$\[ \int \left( 3x^2 + x + \dfrac{1}{x^3} \right) \,dx \] \\ \\ \\ \int 3x^2 \ dx + \int x \ dx + \int \dfrac{1}{x^3} \ dx \\ \\ \\ \boxed{x^3 + \dfrac{x^2}{2} - \dfrac{1}{2x^2} + c}$

Resposta: Quarto item.

Bons estudos :)