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The value of int(2)^(3)(x+1)/(x^(2)(x-1)...

The value of `int_(2)^(3)(x+1)/(x^(2)(x-1))dx` is

A

`log.(16)/(9)+(1)/(6)`

B

`log.(16)/(9)-(1)/(6)`

C

`2log2-(1)/(6)`

D

`log.(4)/(3)-(1)/(6)`

Text Solution

Verified by Experts

The correct Answer is:
B
Let ` l = int _(2)^(3) (x+1)/(x^(2) (x-1)) dx = int _(2)^(3) ((-2)/x - 1/(x^(2)) + 2/(x-1))dx` ,
` = [ -2 log x +1/x +2 log (x-1) ]_(2)^(3)` ,
` = 2 log. 4/3 - 1/6 = log. 16/9 -1/6`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DEFINITE INTEGRALS-MHT CET Corner
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