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Question Number 47062 by maxmathsup by imad last updated on 04/Nov/18

find ∫ (√(((√x)−1)/((√x)+1)))dx

find∫x−1x+1dx

Answered by tanmay.chaudhury50@gmail.com last updated on 04/Nov/18

t^2 =x dx=2tdt ∫(√((t−1)/(t+1))) ×2tdt ∫((2t(t−1))/(√(t^2 −1)))dt ∫((2t^2 −2+2−2t)/(√(t^2 −1)))dt 2∫(√(t^2 −1)) +2∫(dt/(√(t^2 −1)))−∫((d(t^2 −1))/(√(t^2 −1))) 2[(t/2)(√(t^2 −1)) −(1^2 /2)ln∣t+(√(t^2 −1)) ]+2ln∣t+(√(t^2 −1)) ∣−(((t^2 −1)^(1/2) )/(1/2))+c =2[((√x)/2)(√(x−1)) −(1/2)ln∣(√x) +(√(x−1)) ∣]+2ln∣(√x) +(√(x−))1 ∣−(((x−1)^(1/2) )/(1/2))+c

t2=xdx=2tdt∫t−1t+1×2tdt∫2t(t−1)t2−1dt∫2t2−2+2−2tt2−1dt2∫t2−1+2∫dtt2−1−∫d(t2−1)t2−12[t2t2−1−122ln∣t+t2−1]+2ln∣t+t2−1∣−(t2−1)1212+c=2[x2x−1−12ln∣x+x−1∣]+2ln∣x+x−1∣−(x−1)1212+c

Commented by maxmathsup by imad last updated on 05/Nov/18

thank you sir Tanmay.

thankyousirTanmay.

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