#### Question

Evaluate : `int_1^2 1/((x+1)(x+3)) dx`

#### Solution

`int_1^2 1/((x+1)(x+3)) dx`

= `1/2int_1^2(1/(x+1)-1/(x+3))dx`

=`1/2[{log(x+1)}_1^2-{log(x+3)}_1^2]`

=`1/2[(log)3-log2)-(log 5-log4)]`

=`1/2(log3+log4)-(log2+log5)`

=`1/2[log12-log10]`

=`(1/2)log (12/10)`

∴`int_1^2 1/((x+1)(x+3))dx=1/2 log (6/5)`

Is there an error in this question or solution?

#### APPEARS IN

Solution Evaluate : ∫ 2 1 1 ( X + 1 ) ( X + 3 ) D X Concept: Maxima and Minima.