Question Detail
Question
Simplify $\int 3x^2 e^{x^3} dx$.
Correct Answer
Option B is the correct answer.
Detailed Explanation
This integral can be solved using substitution.Let $u = x^3$.Differentiate $u$ with respect to $x$: $du = 3x^2 dx$.Substitute $u$ and $du$ into the integral:$\int e^u du$Integrate with respect to $u$:$e^u + C$Substitute back $u = x^3$:$e^{x^3} + C$
Hint
Look for a part of the integrand whose derivative is also present (or a constant multiple of it).