Question

Помогите пожалуйста найти интегралы?

Answer 1

$Large int_{-2}^{1}{mathrm dx over (11+5x)^3}={1over5}int_{-2}^{1}{mathrm d(11+5x) over (11+5x)^3}={1over5}{(11+5x)^{-2}over -2}|_{-2}^{1}=-{1over10}{1over(11+5x)^2}|_{-2}^{1}=-{1over10}left ( {1over16^2} -{1over 1^2}right )=-{1over10}cdot{-255over256}={255over2560}={51over512}\\ int_{0}^{piover2}cos^5{x}sin{(2x)}mathrm dx=2int_{0}^{piover2}cos^6{x}sin{x}mathrm dx=-2int_{0}^{piover2}cos^6{x}mathrm d{(cos{x})}={-2over7}cos^7{x}|_{0}^{piover2}={-2over7}left ( cos^7{left (piover2 right )}-cos^7{(0)} right )={2over7}$