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Question

 

∫ e^x³•x²dx=

Answer 1

Here, one could simply study the form of the integrand e^{x^3} • x².

Knowing the rules of logarithmic differentiation, he would recognize 

that e^{x^3} differentiates to 3x² • e^{x^3}, very close to the integrand.

Then give a coefficient of 1/3 to e^{x^3} and add a general constant C to gain

e^{x^3}/3 + C as the solution sought.