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

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

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

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

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

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 (

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

) is correct because the integral can be solved by manipulating the integrand and using integration by parts.