Question Number 101178 by bemath last updated on 01/Jul/20

∫ ((((√x)−x)^2 )/x^2 ) dx ?

Answered by bobhans last updated on 01/Jul/20

∫ ((x−2x^(3/2) +x^2 )/x^2 ) dx = ∫(1/x)−(2/(√x)) +1 dx = ln∣x∣ − 4(√x) + x + C it easy..=

Answered by mathmax by abdo last updated on 01/Jul/20

I =∫ ((((√x)−x)^2 )/x^2 )dx changement (√x)=t give x=t^2 ⇒ I =∫ (((t−t^2 )^2 )/t^4 )(2tdt) =2 ∫ ((t^3 (1−t)^2 )/t^4 )dt =2 ∫ ((t^2 −2t+1)/t)dt =2 ∫ (t−2+(1/t))dt =t^2 −4t +2ln∣t∣ +C=x−4(√x)+2ln∣(√x)∣ +C