Question

Помогите решить неопределенный интеграл
$intlimits (5-3x)^2^1 , dx$


Answer 1

$int (5-3x)^{21}dx=[, t=5-3x; ,; dt=-3, dx; ,; dx=-frac{dt}{3}, ]=\\=-frac{1}{3}int t^{21}dt=-frac{1}{3}cdot frac{t^{22}}{22}+C=-frac{1}{66}cdot (5-3x)^{22} +C$

Answer 2

$intlimits {(5-3x)^{21}} , dx = intlimits {(5-3x)^{21}} , d(frac{-3x}{-3})=\ \ =-frac{1}{3}intlimits {(5-3x)^{21}} , d(-3x)=-frac{1}{3}intlimits {(5-3x)^{21}} , d(5-3x)=\\ =-frac{1}{3}*frac{(5-3x)^{21+1}}{21+1}+C=-frac{(5-3x)^{22}}{66}+C=-frac{(3x-5)^{22}}{66}+C$