Задача 35921 ...

vk173500291

2019-04-16 15:47:47

∫ x^(3)dx/ sqrt(x-7)

sova

2019-04-16 16:10:18

Замена
sqrt(x-7)=t
x-7=t^2
x=t^2+7
dx=2tdt

x^3=(t^2+7)^3=t^6+21t^4+147t^2+343)

= ∫ (t^6+21t^4+147t^2+343)*2tdt/t=

=(2t^7/7)+42*(t^5/5)+(147)*t^3/3+343t+C, t=sqrt(x-7)