What is #f(x) = int x^3-x+xe^x dx# if #f(1) = 3 #? Calculus Techniques of Integration Evaluating the Constant of Integration 1 Answer Monzur R. May 1, 2017 #f(x)=1/4x^4-1/2x^2+xe^x-e^x+11/4# Explanation: #f(x)=intx^3-x+xe^x# #dx# Integrate each term separately: #f(x)=1/4x^4-1/2x^2+xe^x-e^x+"c"# #f(1)=1/4(1)^4-1/2(1)^2+1e^1-e^1+"c"=3# #"c"=11/4# #f(x)=1/4x^4-1/2x^2+xe^x-e^x+11/4# 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 1259 views around the world You can reuse this answer Creative Commons License