Question Detail
Question
Simplify ∫ 3x2ex3dx.
Correct Answer
Option B is the correct answer.
Detailed Explanation
To simplify the integral ∫ 3x2ex3dx, use u-substitution.Let u = x3.Then, differentiate u with respect to x: du/dx = 3x2, which means du = 3x2 dx.Substitute u and du into the integral:∫ eu duThe integral of eu with respect to u is eu.∫ eu du = eu + CFinally, substitute back u = x3:ex3 + C.
Hint
Look for a substitution where the derivative of your 'u' matches the remaining part of the integrand.