Question Number 103511 by bemath last updated on 15/Jul/20

∫ (dx/((√x) ((x)^(1/4)  +1))) =__  (a) −((9 (x)^(1/4)  +1)/(18((x)^(1/4)  +1)^9 )) + c   (b) ((9 (x)^(1/4)  +1)/(18((x)^(1/4) +1)^9 )) +c  (c) −((9 (x)^(1/4)  −1)/(18((x)^(1/4)  +1)^9 )) +c  (d) ((9 (x)^(1/4) +1)/(8((x)^(1/4)  +1)^9 )) + c

Commented bybobhans last updated on 15/Jul/20

nothing answer

Answered by bramlex last updated on 15/Jul/20

let t = 1+(x)^(1/4)  ⇒(x)^(1/4)  = t−1  x= (t−1)^4  ∧ (√x) = (t−1)^2   dx = 4(t−1)^3  dt   I= ∫ ((4(t−1)^3  dt)/((t−1)^2 .t ))= 4∫ ((t−1)/t) dt  = 4∫(1−(1/t)) dt   = 4t − 4ln∣t∣ +c   = 4(1+(x)^(1/4) )−4ln∣1+(x)^(1/4)  ∣ + c