$\smallint \,{\left( {\frac{{x + 2}}{{x + 4}}} \right)^2}{e^x}\,dx$ is equal to

${e^x}\,\,\left( {\frac{{x\,\, + \,\,2}}{{x\,\, + \,\,4}}} \right)\,\, + \,\,c$

${e^x}\,\,\left( {\frac{{x\,\, - \,\,2}}{{x\,\, + \,\,4}}} \right)\,\, + \,\,c$

$\left( {\frac{{2\,x{e^x}}}{{x\,\, + \,\,4}}} \right)\,\, + \,\,c$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Analyzing +4 | -1

\int \,{\left( {\frac{{x + 2}}{{x + 4}}} \right)^2}{e^x}\,dx

is equal to

View answer and explanation

Correct option: A

{e^x}\,\,\left( {\frac{x}{{x\,\, + \,\,4}}} \right)\,\, + \,\,c

Option A is correct because the integral simplifies to

{e^x}\,\left( {\frac{x}{{x\,\, + \,\,4}}} \right)\,\, + \,\,c

after applying integration by parts and simplification.