$\smallint \,\,\frac{{{x^2} + \,\,x\,\, - 6}}{{\left( {x - 2} \right)\,\,\left( {x - 1} \right)}}\,\,dx$

$x\,\, + \,\,2\,\,\log \,\,\left( {x - 1} \right)\,\, + \,\,c$

$2x\,\, + \,\,2\,\,\log \,\,\left( {x - 1} \right)\,\, + \,\,c$

$x\,\, + \,\,4\,\,\log \,\,\left( {1 - x} \right)\,\, + \,\,c$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

\int \,\,\frac{{{x^2} + \,\,x\,\, - 6}}{{\left( {x - 2} \right)\,\,\left( {x - 1} \right)}}\,\,dx

View answer and explanation

Correct option: D

x\,\, + \,\,4\,\,\log \,\,\left( {x - 1} \right)\,\, + \,\,c

Option D (

x\\,\\ + \\,4\\,\log \\,\left( {x - 1} \right)\\,\\ + \\,\\,c

) is correct because the integral simplifies to a rational function that can be easily integrated after partial fraction decomposition.