What is f(x) = int x^2e^x-x^2 dx if f(-1) = 5 ?

1 Answer
Oct 29, 2017

f(x)=(x^2-2x+2)*e^x-(x^3)/3+14/3-5e^(-1)

Explanation:

f(x)=int x^2*e^x*dx-int x^2*dx

=(x^2-2x+2)*e^x-(x^3)/3+C

After imposing f(-1)=5 condition,

5e^(-1)+1/3+C=5

Hence C=14/3-5e^(-1)

Thus, f(x)=(x^2-2x+2)*e^x-(x^3)/3+14/3-5e^(-1)

Note: I used tabular integration for first integral.