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Question Number 537 by kth last updated on 25/Jan/15

∫_4 ^5 ((x−2)/((x^2 −4x+3)^3 ))dx

45x2(x24x+3)3dx

Answered by Vishal last updated on 25/Jan/15

let x^2 −4x+3 = t then (x−2) dx = (dt/2)  ⇒ ∫_t_1  ^t_2  (dt/(2(t)^3 )) = (1/2)∫_3 ^8  t^(−3) dt = ((−1)/4)[(1/t^2 )]_3 ^8   ⇒ ((−1)/4) [(1/(64)) − (1/9)] = ((−1)/4) (((−55)/(576))) = ((55)/(2304))

letx24x+3=tthen(x2)dx=dt2t1t2dt2(t)3=1238t3dt=14[1t2]3814[16419]=14(55576)=552304

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