Question

Evaluate the integral using integration by parts where possible
(2-x)e^x dx

Answer 1

Notice that our \(2-x\), if differentiated, will reduce to a constant; our \(e^x\), however, will not. This means we should should treat our integral as (by integration by parts): \(\int(2-x)\,\mathrm{d}(e^x)=(2-x)e^x-\int e^xd(2-x)\)

Answer 2

so I dont need to worry about the (2-x)?

Answer 3

\[\int (2-x)e^x dx=2\int e^xdx -\int xe^xdx\] is a start

Answer 4

first part is pretty obviously \(2e^x\) it is the second integral
\[\int xe^xdx\] that requires parts

Answer 5

you know how to do that?

Answer 6

is it uv-vdu?