Question

Resolvendo a integral $\int\limits ( x^{2} -4x + 1) dx$ obtemos a função
a) F(x) = 2x - 4 + c
b) F (x) = $( x^{3} -4 x^{2} / 2 + x+c$
c) F (x) = $\frac{ x^{3} }{3} -4 x^{2} +x+c$
d) F (x) = $\frac{ x^{3} }{3} -2 x^{2} +x+c$

Answer 1

$F\left(x \right )=\int{\left(x^{2}-4x+1 \right )\,dx}\\ \\ \\ F\left(x \right )=\dfrac{x^{2+1}}{2+1}-4\cdot \dfrac{x^{1+1}}{1+1}+x+C\\ \\ \\ F\left(x \right )=\dfrac{x^{3}}{3}-4\cdot\dfrac{x^{2}}{2}+x+C\\ \\ \\ F\left(x \right )=\dfrac{x^{3}}{3}-2x^{2}+x+C$


Resposta: alternativa $\text{ d) }F\left(x \right )=\dfrac{x^{3}}{3}-2x^{2}+x+C.$