Question

Integrate (sinx)/(sin4x)

Answer 1

@experimentX help?

Answer 2

\[\int {\sin x \over \sin (4x)}dx\]

Answer 3

Yep.

Answer 4

this doesn't look nice ... seems complex terms are involved.
http://www.wolframalpha.com/input/?i=Integrate+sin%28x%29%2Fsin%284x%29&dataset=

i think it's easier to use
\[ \sin x = {e^{ix}-e^{-ix} \over 2i}\]

Answer 5

Uhhh.
I saw that.
But it has a simple answer. Apparently. OR so my book says.

Answer 6

i m just trying....
sin (5x-4x) / sin 4x = (sin 5x cos 4x- cos 5x sin 4x) / sin 4x
the 1st integral will be difficult...

Answer 7

What if we changed the denominator...

So sin(2A)=sin(A+A) = 2sinAcosA

So sin(4x) = sin(2*(2x)) = 2sin(2x)cos(2x)
= 2*(2sinxcosx)cos(2x)
= 4 sinx cosx cos(2x)

Answer 8

Multiply using conjugates.

Answer 9

or you can also simplify the denominator by using trig identity.

Answer 10

cos(2x) = 1 - 2sin^2(x)

Answer 11

u substitute for sin x now and I think it might work out

Answer 12

there if substitution was to be made then it will be u=cos x, du=-sin x dx.

Answer 13

looks like this works
http://www.wolframalpha.com/input/?i=Integrate+cos%284x%29sin%285x%29

Answer 14

@ChmE I got it.
Partial fractions after that.
Thanks!

Answer 15

yw, glad it worked out

Answer 16

Aha. @experimentX Lets try the alter.

Answer 17

sure

Answer 18

yup, but denominator will be something like
\(4u(u^2-1)\sqrt{1-u^2}\)
isn't it ?

Answer 19

*2u^2-1

Answer 20

I didn't get that far. I stopped when he said it worked. It did look to be getting pretty messy

Answer 21

@Hartnn.
Multiply divide by cosx.
Denominatorr is (4(1-t^2)(1-2t^2 )

Answer 22

@experimentX It should be "cot4x not cos4x, right?

Answer 23

got it.

Answer 24

And cot4x is still terrible. http://www.wolframalpha.com/input/?i=Integrate+cot%284x%29sin%285x%29

Answer 25

http://www.wolframalpha.com/input/?i=Integrate+%28e^%28i4x%29%2Be^%28-i4x%29%29%2F2*%28e^%28i5x%29-e^%28-i5x%29%29%2F%282i%29

Answer 26

changing back ei's back to trigonometric form should give that result
check on alternate forms
http://www.wolframalpha.com/input/?i=Integrate+cos%284x%29sin%285x%29

Answer 27

woops!! looks like i forgot to divide by sin 4x

Answer 28

@siddhantsharan have you verified the answer by differentiating?

Answer 29

Yes.
It does work.
Plus the method suggested by ChMe works like a charm. So I dunno what wolfram's doing.

Answer 30

oh!! i never expected a inverse hyperbolic

Answer 31

Seriously.

Answer 32

looks like i shouldn't depend on Wolf anymore!! :(

Answer 33

It's happened like 5-6 times with me now...

Answer 34

hahaha ... serves me right :)

Answer 35

hahaa. :)