Theory question 102
IntegrationEvaluate ∫13 (x − 1)/(x + 1)2 dx.
Show the model answer
Model answer
(x − 1)/(x + 1)² = 1/(x + 1) − 2/(x + 1)².
∫ = [ln(x + 1) + 2/(x + 1)] from 1 to 3 = (ln 4 + ½) − (ln 2 + 1) = ln 2 − ½ ≈ 0.193.
Explanation
Split the fraction first (write x − 1 as (x + 1) − 2).