Question

$\int {(x^2+6x+1)} \, dx$

Answer 1

Olá!

$\int\limits {(x^{2} +6x+1)} \, dx =\\ \\ \int\limits {x^{2} dx+\int\limits {6x dx+\int\limits {dx}=$

$\int\limits {x^{2} dx+6\int\limits {x dx+\int\limits {dx}=$

$\dfrac{x^{3}}{3} +6\cdot\dfrac{x^{2}}{2} +x+C\\ \\ \\ \boxed{\dfrac{x^{3}}{3} +3{x^{2}} +x+C}$

:)

Answer 2

Explicação passo-a-passo:

$\boxed{\int {(f(x)+g(x))} \, dx =\int {f(x)} \, dx + \int {g(x)} \, dx}$

$\int {(x^2)} \, dx+\int {(6x)} \, dx+\int {(1)} \, dx$

$\frac{x^3}{3}+\frac{6x^2}{2} +x=\boxed{\frac{x^3}{3}+3x^2+x+C }$