How do you find the antiderivative of #[e^(2x)/(4+e^(4x))]#? Calculus Introduction to Integration Integrals of Exponential Functions 1 Answer Ratnaker Mehta Aug 3, 2016 #1/4arctan(e^(2x)/2)+C#. Explanation: Let, #I = inte^(2x)/(4+e^(4x))dx#. We take subst. #e^(2x)=t rArr e^(2x)*2dx=dt#. Therefore, #I=1/2int(2*e^(2x)*dx)/{4+(e^(2x))^2}#, #=1/2intdt/(4+t^2) = 1/2*1/2*arctan(t/2)#. Hence, #I=1/4arctan(e^(2x)/2)+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 4788 views around the world You can reuse this answer Creative Commons License