Question

Resolvendo a integral f( x² -4x +1 ) dx obtemos a :função
a)F(x)= 2x - 4 + c
b) F(x)= x³ - 4 x²/2 +x +c
c)F(x)=x³/3 -4x +x+c
d)F(x)=x³/3 - 2x²+x +c

Answer 1

Sabemos que:

$f(x) = x^n\\\\ \boxed{\int = \frac{x^n^+^1}{n+1}}$

Então, temos que:

$f(x)=x^2-4x+1\\\\ \int\ x^2-4x+1\ dx=\\\\ \frac{x^{2+1}}{2+1}-4*(\frac{x^{1+1}}{1+1})+\frac{x^{0+1}}{0+1}\\\\ = \frac{x^3}{3}-\frac{4x^2}{2}+x\\\\ \boxed{\therefore\ \int\ x^2-4x+1\ dx=\frac{x^3}{3}-2x^2+x+C}$