How do you integrate #e^x / sqrt(1-e^(2x)) dx#? Calculus Introduction to Integration Integrals of Exponential Functions 1 Answer Ratnaker Mehta Jun 20, 2016 #arcsin(e^x)+C.# Explanation: We use Method of Substitution : Let #e^x=t#, so that, #e^xdx=dt.# Also, note that, #e^(2x)=t^2.# Hence, #I=inte^x/sqrt(1-e^(2x))dx=int1/sqrt(1-t^2)dt=arcsint=arcsin(e^x)+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 45889 views around the world You can reuse this answer Creative Commons License