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 a simple 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:$\int e^u du$Integrate with respect to $u$:$e^u + C$Finally, substitute $x^3$ back for $u$:$e^{x^3} + C$
Hint
Look for a part of the integrand whose derivative is also present in the integrand. This suggests a u-substitution.