Question

Calcule:
$\int ({x^{3}-4 x^{2} -2x+1) } \, dx$

Answer 1

$\boxed{\boxed{\int x^{n}dx=\dfrac{x^{n+1}}{n+1}+C~~~,~~~n\neq-1}}$

$\boxed{\boxed{\int[f(x)+g(x)+...+z(x)]dx=\int f(x)dx+\int g(x)dx+..+\int z(x)dx}}$

$\boxed{\boxed{\int kf(x)dx=k\int f(x)dx~~~~~~~onde~k~\'e~constante}}$
______________________________

$\int(x^{3}-4x^{2}-2x+1)dx=\int x^{3}dx-\int4x^{2}dx-\int2xdx+\int1dx\\\\\int(x^{3}-4x^{2}-2x+1)dx=\frac{x^{4}}{4}-4\int x^{2}dx-2\int xdx+\int x^{0}dx\\\\\int(x^{3}-4x^{2}-2x+1)dx=\frac{x^{4}}{4}-4\frac{x^{3}}{3}-2\frac{x^{2}}{2}+\frac{x^{1}}{1}+C\\\\\\\boxed{\boxed{\int(x^{3}-4x^{2}-2x+1)dx=\dfrac{x^{4}}{4}-\dfrac{4}{3}x^{3}-x^{2}+x+C}}$