Question

Помогите пожалуйста, прошу, срочно )

Answer 1

$displaystyle 1. int^3_2 frac{1+x^5}{x^4}dx= int^3_2 frac{x^5}{x^4}dx+ int^3_2 frac{1}{x^4}dx= int^3_2xdx- frac{1}{3x^3}=$
$displaystyle = frac{x^2}{2}- frac{1}{3x^3}= frac{3x^5-2}{6x^3} bigg|^3_2= frac{729-2}{162}- frac{96-2}{48} = frac{727}{162}- frac{94}{48}=$
$displaystyle = frac{34896-15228}{7776}= frac{6556}{2592}= frac{1639}{648}$

$displaystyle 2. int^{ frac{pi}{6}}_{ frac{pi}{8}} 2 cdot frac{1}{cos^2x}dx=2 cdot frac{1}{2}tg2x=tg2x bigg|^{ frac{pi}{6}}_{ frac{pi}{8}} =tg frac{pi}{3}-tg frac{pi}{4}= sqrt{3}-1$

$displaystyle 3. int^1_0 x^2(2-x^3)^4dx= frac{(x^3-2)^5}{15} bigg|^1_0=- frac{1}{15}-(- frac{32}{15})= frac{31}{15}$