Many problem Solvers of Integral Calculus often use a long method to solve integration problems whose integrand is a Natural Exponential Function.This article will show a short method to evaluate such an integral.
Things You Will NeedPaper, pencil, and a creative mind.
We are going to use an example problem to Illustrate the short method of evaluating an Integral whose Integrand is a Natural exponential function. To see the problem/Integral, Please click on the Image.
3x2 is the Exponent of e, and the Derivative of 3x2 is 6x. We will look to see if the Derivative of the Exponent of the Base e is being multiplied by the Natural Exponential Function. Please click on the Image for a better understanding.
Tips & WarningsDo not assume that this method will work for all Integration problems of this form. It is the reader's responsibility to understand when the mental U-Substitution method can be applied.