Posted by Cynthia on Tuesday, August 7, 2012 at 5:52pm.
(1/2) (2 x e^2x dx)
let z = 2 x
then dz = 2 dx or dx = dz/2
so
(1/2) z e^z (dz/2)
(1/4) z e^z dz
but
int z e^z dz = e^z (z-1) + c
so
(1/4)e^z(z-1) + c
(1/4) e^2x (2x-1) + c
(1/2) x e^2x - (1/4) e^2x + c
so c
e^3x cosh 2x dx
cosh 2x = (1/2)(e^2x + e^-2x)
so
(1/2)(e^3x)(e^2x + e^-2x)dx
= (1/2)(e^5x + e^x)dx
(1/10) e^5x + (1/2) e^x + c
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