Question

∫sin(-2x-1)cos(2x-1)

Answer 1

sin(2x) = 2sin(x)cos(x)
sin(2x)/2 = sin(x)cos(x)
sin(2(-2x-1))/2 = sin(-2x-1)(cos(-2x-1)
sin(-4x-2) = sin(-2x-1)cos(-2x-1)
integrate the left hand side

Answer 2

Slight mistake there zzr0ck3r

Answer 3

fix it:)

Answer 4

I don't know integration. I'm just saying you put cos(-2x-1) and it's cos(2x-1). I'm learning integration next week lol.

Answer 5

ahh I forgot the 2
sin(-4x-2)/2 = sin(-2x-1)cos(-2x-1)

Answer 6

ohh woops, good call. well that changes everything....lol

Answer 7

Wonder if the extra negative inside of the sin angle is supposed tobethere. *kicks site* finally working again.

Answer 8

yeah im thinking the same thing, or if the one on the right is missing it

Answer 9

seems to odd...

Answer 10

I was thinking the same thing Psymon.

Answer 11

lol

Answer 12

Can't you use the identity for sin(a)cos(b)?

Answer 13

No reason to.

Answer 14

there are lots of ways to do it, I was going for the easy one.

Answer 15

I thought the (1/2)sin2x one reeked of win, so let's stick to that.

Answer 16

then we are done
\[\int sin(-2x-1)cos(-2x-1)dx=\frac{1}{2}\int sin(-4x-4)dx = \frac{1}{8}cos(-4x-2)\]

Answer 17

u=2x+1?

Answer 18

not that it matters, im just trying to learn it:)

Answer 19

slight mistake there lol

Answer 20

oh yeah the signs dont match

Answer 21

You with us now dumbcow lol

Answer 22

we are thinking his question has a typo, and he medaled me so maybe so...no idea

Answer 23

Which is why we just do some science and throw in some magic extra negative and pretend they are the same angle.

Answer 24

yeah
http://www.wolframalpha.com/input/?i=integrate+-sin%282x%2B1%29cos%282x-1%29+dx

prob need to expand whole thing using sum/difference identity

Answer 25

that's odd...sin(2) lol

Answer 26

Haha, I like the random sin(2)

Answer 27

Alarm bells ringing lol

Answer 28

if this is from a regular textbook....all bets on typo :)

Answer 29

Or a cruel person giving out hw?

Answer 30

@Aoi please put us out of our misery

Answer 31

青いさん D:

Answer 32

Same to you psymon

Answer 33

x_x Okay, leaving then

Answer 34

lol

Answer 35

Note to self: learn pinyin.

Answer 36

'Aoi' sounds like something a samurai would say before comitting hara kiri.

Answer 37

Take u=cos(2x-1)

Answer 38

du=-2sin(2x-1)

Answer 39

U get
sin(-(2x-1))=-sin(2x-1)
Multiple Numerator and denominator by 2 and take (1/2) outside!!

Answer 40

we are in no rush just hit enter when you are done:)

Answer 41

\[{1/2}\int\limits u du\]

Answer 42

Integrate the function........
Substitute u=cos(2x-1) and u get the answer,I guess!!

Answer 43

I hope thats right @zzr0ck3r @Mandre @Psymon @Aoi