What is #f(x) = int x^2e^(x-1)-x^3e^-x dx# if #f(2) = 7 #?

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May 25, 2018

Answer:

your integral is given by
#x^3e^-x+x^2e^(x-1)+3x^2e^(-x)-2xe^(x-1)+6e^(-x)x+2e^(x-1)+6e^(-x)+C#

Explanation:

I have got this after several times integrating by parts.
We get #C# by the following equation
#38e^(-2)+2e+C=7#

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