What is f(x) = int 1/x-e^x dx if f(1) = 0 ? Calculus Techniques of Integration Evaluating the Constant of Integration 1 Answer Alan N. May 5, 2016 f(x)=ln(x)-e^x+e Explanation: f(x)= int(1/x-e^x)dx =int1/xdx-inte^xdx (Linearity) int1/xdx = ln(x) (Standard integral) inte^x = e^x (Exponential rule) Therefore: f(x) = ln(x)-e^x +C (Where C is the constant of integration) We are told that f(1)=0 Thus: ln(1)-e^1+C=0 0 - e +C =0 C=e Hence: f(x)=ln(x)-e^x+e 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 1649 views around the world You can reuse this answer Creative Commons License