The value of $\smallint \,\,\frac{{{e^{5{{\log }_e}x}}\,\, - \,\,{e^{4{{\log }_e}x}}}}{{{e^{3{{\log }_e}x}}\,\, - \,\,{e^{2{{\log }_e}x}}}}\;\,\,dx$ is

$\frac{{{x^2}}}{2}\,\, + \,\,c$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

The value of

\int \,\,\frac{{{e^{5{{\log }_e}x}}\,\, - \,\,{e^{4{{\log }_e}x}}}}{{{e^{3{{\log }_e}x}}\,\, - \,\,{e^{2{{\log }_e}x}}}}\;\,\,dx

View answer and explanation

Correct option: C

\frac{{{x^3}}}{3}\,\, + \,\,c

Option C (

\frac{{{x^3}}}{3} + c

) is correct because it is the result of simplifying the expression and then integrating.