Question

integrate by parts: (sin^2(x))(cos^4(x))

Answer 1

i would replace sin^2(x) by (1-cos(2x))/2
and cos^4(x) by [(1+cos(2x))/2]^2

Answer 2

thats what i have so far

Answer 3

it is a good start..
so then you have

(1/8)(1-cos(2x))(1+2cos(2x)+cos^2(2x))
(1/8)(1+cos(2x)-cos^2(2x)-cos^3(2x))

Answer 4

did you get the 1/8 by pulling out the 1/2's

Answer 5

the first two terms are easy to integrate .. now we have to deal with
-cos^2(2x)-cos^3(2x)

for the cos^2(2x) you can use now (cos(4x)+1)/2

and for the cos^3(2x) you can use (1-sin^2(2x))(cos(2x))

Answer 6

yes .. that's how i got the (1/8)

Answer 7

sorry i'm kinda slow at this...ahahah trying to understand how to do it

Answer 8

integration by u-subt told me the final anwer is 1/3*(tan(x))^3

Answer 9

i gottah do it by parts

Answer 10

answer*

Answer 11

i got (1/16)[x-(1/4)sin(4x)+(1/3)sin^3(2x)] + C

Answer 12

sorry back track

Answer 13

i dont understand how you got (1/8)(1-cos(2x))(1+2cos(2x)+cos^2(2x))

Answer 14

is it because you squared it?

Answer 15

i think int by parts it doesnt work here, but u-sub will work to solve..

Answer 16

ok

Answer 17

can u do it

Answer 18

yes i think so

Answer 19

the way i wrote works here for sure..
i got (1/8)(1-cos(2x))(1+2cos(2x)+cos^2(2x)) after the squaring of the second term

Answer 20

after squaring it, i got that too (1/8)(1-cos(2x))(1+2cos(2x)+cos^2(2x)).

Answer 21

now i'm trying to understand how you got (1/8)(1+cos(2x)-cos^2(2x)-cos^3(2x))

Answer 22

@Collsector, can u show all steps from u use the formula int(udv)=uv-int(vdu), please

Answer 23

ups, sorry @Coolsector *

Answer 24

i gave the steps up there..

Answer 25

there is no integration by parts here

Answer 26

yes. i realized its not integration by parts but integrating products of sines and cosines

Answer 27

so, u dont use by parts too ?

Answer 28

omg i'm so slow. just figured out how you got (1/8)(1+cos(2x)-cos^2(2x)-cos^3(2x))

Answer 29

just multiplying ( )( )

Answer 30

yea. i just ket multiplying it wrong xP

Answer 31

so how is it going for you ?

Answer 32

for just proportion from me