`int (5x + 1)/((2x + 1)(x-1))dx` Evaluate the integral

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kspcr111 | In Training Educator

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`int (5x + 1)/((2x + 1)(x-1))dx`

sol:

`int (5x + 1)/((2x + 1)(x-1))dx`

by partial fraction we get

= `int (((A/(2x + 1))+( B/(x-1))) dx`

compare the numerators as denominators are equal

`5x+1` =` A(x-1) +B(2x+1)`

on comparing the co-efficients of x and the constants we get

`A= 1` , `B=2`

= `int (((1/(2x + 1))+( 2/(x-1))) dx`

= `int ((1/(2x + 1)) dx+ int ( 2/(x-1)) dx`

=` (ln(2x+1)/2) +2* ln(x-1) +C`

:)