Question

int e^x cos(2x)

Answer 1

unintegrable! no dx :P haha

Answer 2

but seriously...if that's the whole question it's unintegrable

Answer 3

\[\int\limits e^{x} \cos \left( 2x \right) dx\]use integration by parts

Answer 4

int e^x cos(2x)
=int cos(2x) d(e^x)
=(e^x)(cos(2x))-int (e^x)d(cos2x)
=(e^x)(cos2x)+2inte^xsin2xdx
=(e^x)(cos2x)+2intsin2x(e^x)
=(e^x)(cos2x)+2(sin2x)(e^x)-2inte^x d(sin2x)
=(e^x)(cos2x)+2(sin2x)(e^x)-4int(e^x)cos2x dx
5int(e^x)(cos2x)=(e^x)(cos2x)+2(sin2x)(e^x)
int(e^x)(cos2x)=(1/5)((e^x)(cos2x)+2(sin2x)(e^x))
=(1/5)(e^x)(cos2x +2sin2x) +C

Answer 5

integration by parts

u = e^x dv = cos(2x)
du = e^x v = 1/2 sin(2x)

you will have to do parts again ...

Answer 6

yea!!! thats exactly what i got!!! thanks