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Question Number 171038 by Mastermind last updated on 06/Jun/22

Answered by MJS_new last updated on 07/Jun/22

∫_4 ^9 ((x+1)/(x+2(√x)−3))dx=∫_4 ^9 ((x+1)/(((√x)+1)^2 −4))dx= [t=(√x)+1 → dx=2(√x)dt] =2∫_3 ^4 (((t−1)(t^2 −2t+2))/(t^2 −4))dt= =∫_3 ^4 (2t−6+((15)/(t+2))+(1/(t+2)))dt= =[t^2 −6t+15ln ∣t+2∣ +ln ∣t−2∣]_3 ^4 = =1+16ln 2 +15ln 3 −15ln 5

∫94x+1x+2x−3dx=∫94x+1(x+1)2−4dx=[t=x+1→dx=2xdt]=2∫43(t−1)(t2−2t+2)t2−4dt==∫43(2t−6+15t+2+1t+2)dt==[t2−6t+15ln∣t+2∣+ln∣t−2∣]34==1+16ln2+15ln3−15ln5

Commented by peter frank last updated on 07/Jun/22

thank you

thankyou

Answered by GalaxyBills last updated on 07/Jun/22

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