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Question
Fill in the blank : `int_2^3 x/(x^2 - 1)*dx` = _______
Solution
Let I = `int_2^3 x/(x^2 - 1)*dx`
Put x2 – 1 = t
∴ 2x·dx = dt
∴ x·dx = `(1)/(2)*dt`
When x = 2, t = 22 – 1 = 3
When x = 3, t = 32 – 1 = 8
∴ I = `int_3^8 (1)/"t"*"dt"/(2)`
= `(1)/(2)int_3^8 "dt"/"t"`
= `(1)/(2)[log |"t"|]_3^8`
= `(1)/(2)(log 8 - log 3)`
∴ I = `(1)/(2) log (8/3)`.
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