What is f(x) = int 5x-2xe^(x)dx if f(0)=-2 ? Calculus Techniques of Integration Evaluating the Constant of Integration 1 Answer Cem Sentin Jul 11, 2017 f(x)=int5x*dx-int2x*e^x*dx =5/2*x^2-(2x*e^x-int2e^x*dx) =5/2*x^2-(2x-2)*e^x+C Let x=0, C+2=-2, hence C=-4. Thus, f(x)=5/2*x^2-(2x-2)*e^x-4 Explanation: 1) Take integral. 2) Impose f(0)=-2 condition. Answer link Related questions How do you find the constant of integration for intf'(x)dx if f(2)=1? What is a line integral? What is f(x) = int x^3-x if f(2)=4 ? What is f(x) = int x^2+x-3 if f(2)=3 ? What is f(x) = int xe^x if f(2)=3 ? What is f(x) = int x - 3 if f(2)=3 ? What is f(x) = int x^2 - 3x if f(2)=1 ? What is f(x) = int 1/x if f(2)=1 ? What is f(x) = int 1/(x+3) if f(2)=1 ? What is f(x) = int 1/(x^2+3) if f(2)=1 ? See all questions in Evaluating the Constant of Integration Impact of this question 1378 views around the world You can reuse this answer Creative Commons License