$\smallint \,\,\frac{{dx}}{{\sqrt {\left( {1 - x} \right)\,\,\left( {x - 2} \right)} }}$ is equal to

${\sin ^{ - 1}}\,\,\left( {2x\,\, + \,\,5} \right)\,\, + \,\,c$

${\sin ^{ - 1}}\,\,\left( {3\,\, - \,\,2x} \right)\,\, + \,\,c$

${\sin ^{ - 1}}\,\,\left( {5\,\, - \,\,2x} \right)\,\, + \,\,c$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

\int \,\,\frac{{dx}}{{\sqrt {\left( {1 - x} \right)\,\,\left( {x - 2} \right)} }}

is equal to

View answer and explanation

Correct option: A

{\sin ^{ - 1}}\,\,\left( {2x\,\, - \,\,3} \right)\,\, + \,\,c

Option A (

{\sin ^{ - 1}}\,\,\left( {2x\, - \,3} \right)\,\,+ \,c

) is correct because it is the result of completing the square and applying the standard integral formula for arcsine.