Question

HELP ME ?

integral 2x^2+x^3+42

Answer 1

Olá

$\displaystyle \int (2x^2+x^3+42)dx \\ \\ \\ \text{Vamos "quebrar" essa integral em 3 integrais} \\ \\ \\ \int 2x^2dx~~ ~+\int x^3dx~~~+\int 42dx \\ \\ \\ \text{Tira as constantes de "dentro" das integrais} \\ \\ \\ 2\int x^2dx~~ ~+\int x^3dx~~~+42\int dx \\ \\ \\ \text{Resolvendo as integrais}$

$2\cdot\left.\left(\dfrac{x^{2+1}}{2+1}\right)~~+\left.\left(\dfrac{x^{3+1}}{3+1}\right)~~+42\left.\left(\dfrac{x^{0+1}}{0+1}\right)$

$\displaystyle \boxed{= \frac{2x^3}{3} + \frac{x^4}{4} +42x+C}$