How do you integrate #y=xe^(-x)#? Calculus Introduction to Integration Integrals of Exponential Functions 1 Answer Eddie Jul 4, 2016 #= -e^{-x} (x +1) + C# Explanation: #int dx qquad x e^{-x}# IBP: #int u v' = uv - int u'v# here #u = x, u' = 1# #v' = e^{-x}, v = - e^{-x}# so #-x e^{-x} - int dx qquad (-e^{-x})# #= -x e^{-x} - (e^{-x}) + C# #= -e^{-x} (x +1) + C# Answer link Related questions How do you evaluate the integral #inte^(4x) dx#? How do you evaluate the integral #inte^(-x) dx#? How do you evaluate the integral #int3^(x) dx#? How do you evaluate the integral #int3e^(x)-5e^(2x) dx#? How do you evaluate the integral #int10^(-x) dx#? What is the integral of #e^(x^3)#? What is the integral of #e^(0.5x)#? What is the integral of #e^(2x)#? What is the integral of #e^(7x)#? What is the integral of #2e^(2x)#? See all questions in Integrals of Exponential Functions Impact of this question 70934 views around the world You can reuse this answer Creative Commons License