$\int x^2 e^{x^3} \cos \left(e^{x^3}\right) d x$ is equal to
Answer & explanation
Correct answer: option 3
We have,
$I=\int x^2 e^{x^3} \cos \left(e^{x^3}\right) d x=\frac{1}{3} \int \cos \left(e^{x^3}\right) 3 x^2 e^{x^3} d x$
$\Rightarrow I =\frac{1}{3} \int \cos \left(e^{x^3}\right) d\left(e^{x^3}\right)=\frac{1}{3} \sin \left(e^{x^3}\right)+C$