Question Detail
Question
Simplify the integral $\int 3x^2 e^{x^3} dx$.
Correct Answer
Option B is the correct answer.
Detailed Explanation
This integral can be solved using u-substitution.Let $u = x^3$.Then, find the differential $du$: $du = \frac{d}{dx}(x^3) dx = 3x^2 dx$.Substitute $u$ and $du$ into the integral:$\int e^u du$The integral of $e^u$ with respect to $u$ is $e^u + C$.Substitute back $u = x^3$:$e^{x^3} + C$.
Hint
Look for a part of the integrand whose derivative is also present in the integrand.