Integration Pros! Can you integrate this? tanxtan2xtan3x dx .:Resolved:.

[voidflux]

Hello everyone! I was wondering if anyone knew how to integrate the following integral,

//Since I don't know how to make an integral sign, i'll use 'S'

S (tanx)(tan2x)(tan3x) dx;

The answer is, 
(1/3)ln(4cos(x)^2-3)-(1/2)ln(2cos(x)^2-1)-(2/3)ln(cos(x));

Any idea how to get there? Thanks!

I got that answer from the math program maple 9

[fundu]

Replace tan 2x and tan3x with their corresponding values in terms of tan x and tan x ^ 2 and then multiply the terms and integrate them separately. Its not tough. But typing down the method is really tough

[voidflux]

Thanks for the reply, but i was confused on what this ment,

Replace tan 2x and tan3x with their corresponding values in terms of tan x and tan x ^ 2

Can you explain what the corresponding values are?
Thanks!

[prog_tom]

∫tanx tan2x tan3x dx =

∫(sinx/cosx)(2tanx/1-tan^2x)(tanxtan2x/1-tanxtan2x)dx

use u subsituation for cos: u = cos x

And another 30 steps on my proof here...

Btw, where did you get the problem? Someone asked this on another forum too.

[voidflux]

really do they happen to have the answer? heh my calc teacher made us do it, calc II! Thanks for the process though!

[prog_tom]

Originally posted by voidflux
really do they happen to have the answer? heh my calc teacher made us do it, calc II! Thanks for the process though!

If you want, post your email so I can send you a picture of the 30+ line proof.

[voidflux]

thanks!
[email protected]

[fundu]

The expansion of tan 2x was correct but I am afraid that expansion of tan 3x is may be wrong. Just check that in a math book. Gone are the days of my college when I used 2 remember the formula. That is why didn't sent U the expansions.

But my calculus teaching experience says that this is the smallest and best way 2 solve this problem.

[prog_tom]

Originally posted by fundu
The expansion of tan 2x was correct but I am afraid that expansion of tan 3x is may be wrong. Just check that in a math book. Gone are the days of my college when I used 2 remember the formula. That is why didn't sent U the expansions.

But my calculus teaching experience says that this is the smallest and best way 2 solve this problem.

If expansion for tan2x is correct then expansion for tan3x is correct as well, grasshoper.

[voidflux]

Thanks for the responces guys! and thanks for the proof Tom!