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 ).Then, differentiate ( u ) with respect to ( x ): ( du = 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 function and its derivative within the integrand. The exponent \( x^3 \) is a good candidate for substitution.