Question

найти первообразную функции f(x)=x^3-4x-3​

Answer 1

$\displaystyle\bf\\f(x)=x^{3} -4x-3\\\\\\F(x)=\frac{x^{4} }{4} -4\cdot\frac{x^{2} }{2} -3x+C\\\\\\\boxed{F(x)=\frac{x^{4} }{4} -2x^{2} -3x+C}$

Answer 2

$f(x) = x {}^{n} \: \: \: \: \: \: \: \: \: \: - >F(x) = \frac{ {x}^{n + 1} }{n + 1} \\ f(x) = k \: \: \: \: \: \: \: \: \: \: - > F(x) = kx \\ \\ f( x) = {x}^{3} - 4x - 3 \\ F(x) = \frac{ {x}^{3 + 1} }{3 + 1} - \frac{4 {x}^{1 + 1} }{1 + 1} - 3x + C = \\ = \frac{ {x}^{4} }{4} - 2 {x}^{2} - 3x + C$