Question

Evaluate the Integral

Answer 1

\[\int\limits_{0}^{1/2} (xe ^{2x}/(1+2x)^{2}) dx\]

Answer 2

oh this looks fun

Answer 3

too bad I'm trying to eat lunch, the cool problems always show up when I'm busy :/

Answer 4

there is such a thing as a working lunch break lol

Answer 5

That's what I try to tell myself ;)

Answer 6

my hunch before I eat is to say\[u=1+2x\implies x=\frac12(u-1)\implies 2x=(u-1)\]\[du=2dx\implies dx=\frac12du\]bounds change to u=1 and u=2 so we get\[\frac14\int_1^2\frac{(u-1)e^{u-1}}{u^2}du\]and maybe some integration by parts or something...
ok eating now :)

Answer 7

hmmm ok i will start there and work it through. i just never know where to start. thanks!