Question

Помогите с интегралами

Answer 1

1) $intlimits {( frac{4}{ x^{5}}-(1-2x)^3)} , dx = intlimits {(4x^{-5}-1+4x-4 x^{2})} , dx =$
$=intlimits {4x^{-5}} , dx -intlimits {1} , dx +intlimits {4x} , dx -$
$-intlimits {4 x^{2}} , dx = 4* frac{1}{-4} x^{-4}-x+4* frac{1}{2}x^2-4* frac{1}{3} x^{3}+C=$
$=- x^{-4}-x+2}x^2- frac{4}{3} x^{3}+C$

2) $intlimits {(x+ frac{2}{cos ^{2}x}-1)} , dx = intlimits {x} , dx + intlimits {frac{2}{cos ^{2}x}} , dx - intlimits {1} , dx =$
$= frac{1}{2} x^{2} + 2tgx - x +C=$

3) $intlimits {( frac{1}{2}sin frac{x}{2}- 3x^{2})} , dx = intlimits {frac{1}{2}sin frac{x}{2}} , dx - intlimits {3x^{2}} , dx =$
$intlimits {sin frac{x}{2}} , d{ frac{x}{2} } - 3 intlimits {x^{2}} , dx =-cos frac{x}{2} -3* frac{1}{3} x^{3} +C=-cos frac{x}{2}- x^{3} +C$