$\int(x+1)^2 e^x d x$ is equal to
Answer & explanation
Correct answer: option 4
We have,
$I=\int(x+1)^2 e^x d x=\int e^x\left(x^2+2 x\right) d x+\int e^x d x$
$\Rightarrow I=e^x x^2+e^x+C=e^x\left(x^2+1\right)+C$
$\int(x+1)^2 e^x d x$ is equal to
Correct answer: option 4
We have,
$I=\int(x+1)^2 e^x d x=\int e^x\left(x^2+2 x\right) d x+\int e^x d x$
$\Rightarrow I=e^x x^2+e^x+C=e^x\left(x^2+1\right)+C$