Question Number 11406 by tawa last updated on 24/Mar/17

Evaluate:       ∫_( 1) ^( 3)   ((x − 1)/((x + 1)^2 )) dx

Answered by sm3l2996 last updated on 24/Mar/17

((x−1)/((x+1)^2 ))=(a/(x+1))+(b/((x+1)^2 ))  b=−2 ; a=1  I=∫_1 ^3 ((x−1)/((x+1)^2 ))dx=∫_1 ^3 (dx/(x+1))−2∫_1 ^3 (dx/((x+1)^2 ))  =[ln∣x+1∣]_1 ^3 +2[(1/(x+1))]_1 ^3   =ln(2)−(1/2)

Commented bytawa last updated on 24/Mar/17

God bless you sir.