How do you find the antiderivative of ((2x)e^(3x))? Calculus Introduction to Integration Integrals of Exponential Functions 1 Answer Ratnaker Mehta Aug 3, 2016 1/9*(3x-1)*e^(3x)+C. Explanation: Let, I=int2xe^(3x)dx rArr I=2intxe^(3x)dx. To find I, we will use the following Rule of Integration by Parts : intuvdx=uintvdx-int{(du)/dxintvdx}dx. We take, u=x, so, (du)/dx=1, &, v=e^(3x), so, intvdx=1/3e^(3x). So, I=x*1/3e^(3x)-int{1*1/3e^(3x)}dx =x/3e^(3x)-1/3inte^(3x)dx =x/3e^(3x)-1/3*1/3e^(3x) :. I = 1/9*(3x-1)*e^(3x)+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 4233 views around the world You can reuse this answer Creative Commons License