Question

Найдите первообразную.
$f(x) = frac{9 {x}^{2} + 4x + 7x }{x}$
$f(x) = frac{2}{ sqrt{x} } - frac{5}{ {x}^{8} }$

Answer 1

$intlimits {frac{9x^2+4x+7x}x , dx = intlimits {9x+4+7} , dx =intlimits {9x+11} , dx=frac{9x^2}2+11x+C$

$intlimits{frac{2}{sqrt{x}}-frac{5}{x^8} , dx = intlimits{2x^{-frac{1}2}-5x^{-8} , dx =2*frac{x^{-frac{1}2+1}}{-frac{1}2+1}-5*frac{x^{-8+1}}{-8+1}+C=$
$=4x^{frac{1}2}+frac{5}7x^{-7}+C$