Question

∫cos(y)e^-y dy integrate by parts.

Answer 1

you need to build "loop"...
let u=cosy & dv=e^(-y)
then: du=-siny v=-e^(-y)
\[=-e ^{-y}cosy-\int\limits_{}^{}siny*e ^{-y}dy\]
do it one more time..

Answer 2

Or use the chain rule!

Answer 3

you'll get:
u=siny du=cosy
dv=e^(-y) and v=-e^(-y)
\[=-e ^{-y}cosy +e ^{-y}siny - \int\limits_{}^{}cosy*e ^{-y}dy\]
so, you got on right side your original integral !

Answer 4

then:
\[2\int\limits_{}^{}cosy*e ^{-y}dy=e ^{-y}siny - e ^{-y}*cosy\]
divide by 2 both side & you got your answer :)

Answer 5

oh I get it.

Answer 6

Lets not give the complete answer, give one step and ask them to solve the rest :)

Answer 7

I forgot to put constant... sorry. please add to the final answer

Answer 8

Mashy - I agree! sorry...

Answer 9

cause its still an equation, so you move it to te other side and its obvious. Had got as far as the loop and didn't know where to go forom there. Thank you much :)

Answer 10

Sorry for bad spelling there, was typing quickly.

Answer 11

no problem...
that is the "trick" that you can use in similar cos/sin complex integral problems.
Just remember this one for the next time :))

Answer 12

I will, thanks again