Question

Indefinite Integral:

Answer 1

\[\int\limits_{?}^{?} e ^{x} + 4xe ^{2x} / xe ^{x} dx\]

Answer 2

you must specify a bit more

is it

\[\frac {(e^x + 4xe ^{2x} ) } { xe^x} \]

or

\[e^x +\frac{ [ 4xe ^{2x}] } {xe^x} \]

Answer 3

either way it will involve you cancelling factors of e^(x) [ remember that e^(2x) =[ e^(x) ]^2

Answer 4

if its the first one then you get \[\frac{1}{x} + 4e^x\]

which can be integrated easily as ln|x| +4e^x +C

Answer 5

if its the second one then you will get

e^x +4e^x = 5e^x

which integrates as 5e^x +C