How do you integrate #int 6^x-2^xdx# from #[1,e]#? Calculus Introduction to Integration Integrals of Exponential Functions 1 Answer Narad T. Dec 19, 2016 The answer is #=6^e/ln6-2 ^e/ln2-6/ln6+2/ln2=62.8129# Explanation: Let #u=6^x# Then, #lnu=xln6# #u=e^(xln6)# Let #v=2^x# #lnv=xln2# #v=e^(xln2)# Therefore #int_1 ^e(6^x-2^x)dx# #=int_1 ^e(e^(xln6)-e^(xln2))dx# #= [e^(xln6)/ln6-e^(xln2)/ln2 ]_1^e # #= [6^x/ln6-2^x/ln2 ]_1 ^e # #=(6^e/ln6-2^e/ln2)-(6/ln6-2/ln2)# #=6^e/ln6-2 ^e/ln2-6/ln6+2/ln2=62.8129# 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 1640 views around the world You can reuse this answer Creative Commons License