Question Number 103846 by Dwaipayan Shikari last updated on 17/Jul/20

∫(dx/(x^(1/3) +2))

Commented byDwaipayan Shikari last updated on 17/Jul/20

∫((3u^2 du)/(u+2))=∫((3u^2 −12)/(u+2))+((12)/(u+2))=∫3u−6+12log(x^(1/3) +2)=(3/2)x^(2/3) −6x^(1/3) +12log(x^(1/3) +2)+C

Commented byPRITHWISH SEN 2 last updated on 17/Jul/20

x=t^3 ⇒ dx=3t^2 dt  ∫((3t^2 dt)/(t+2))=3 ∫(((t+2)^2 −4(t+2)+4)/((t+2)))dt  =3{∫(t+2)dt−4∫dt+4∫(dt/(t+2))