Intergration please solve intergral tanx^3 dx

- anonymous

Intergration please solve intergral tanx^3 dx

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- amistre64

odd degree trig functions; I think its easier to split them up into groups of something...

- anonymous

Re-write it as ∫tan^2(x)*tan(x) dx ---> ∫(sec^2(x)-1)*tan(x) dx = ∫sec^2(x)tan(x) - tan(x) dx. Let u=tan(x).

- anonymous

well, it is quite simple actually, just wait a minute and sstarica will show you

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- anonymous

re-write it and you'll get :\[\int\limits_{}^{}sinx^3/cosx^3 dx\]
use u substitution for cosx^3 ^_^
give it a try :)

- anonymous

LOL andy :D

- amistre64

Here, use this :)

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- anonymous

oh, and ssarica, gratz on making a Superstar, I guess I cant call you starlet anymore

- anonymous

lol, call me whatever you want and thank you ^_^, some of the fanning came from you :)

- anonymous

yup, whole 4 fannings

- anonymous

amistre! are you encouraging students on using calculators instead of thinking about it?!

- amistre64

at 101 fans you get to be a "hero"....its a shame really, all that work just to become a sandwich....

- anonymous

different times, different accounts, but same me

- anonymous

:) I don't really care much about the fanning process

- amistre64

the mr proffesor is more of an "exercise" in math than it is a calculator :)

- anonymous

lol, anyway did you understand it deidre? ^_^

- anonymous

@sstarica: I'm not sure if your method works, it ends up giving you -1/3 * ∫1/cos^5(x) dx. :/

- amistre64

2x6=?
12 (green light)

- anonymous

for reals? let me try

- anonymous

Whoops, not quite..

- anonymous

no lol , it works!

- anonymous

Oh, sorry. Thought you typed something else ;P

- anonymous

wait, you're right it doesn't work ^^" sorry for the mess again diedre, ignore my answer. Thank you Quantum ^_^

- anonymous

deidre is away, geting some hotdogs for me and me

- anonymous

Now let me check if my answer works...xD

- anonymous

so dont worry, you have some time to clear the mess before he comes back

- anonymous

\[du = -3x^2sinx^3dx\] which is wrong. you can't substitute it there, my dearest apologies ^^"

- anonymous

Ah, let me expand my answer to make it clearer:
∫tan(x)sec^2(x) dx - ∫tan(x) dx. In the first integral, let u=tan(x), and in the second it integrates cleanly. :P

- anonymous

why did you put tanxsec^2x? where did you get it from

- anonymous

x^3 acts as an angle here

- anonymous

and not the power of tan :)

- anonymous

ok, guys, I am about to go to sleep, just going to workout abit and maybe eat something and i am off.

- anonymous

same, I'm tired

- anonymous

oh, nice, so we are going to beds together again

- anonymous

anyway, solve the question and I'm off to bed, sorry ^_^

- anonymous

I'm going to bed ALONE >_>

- anonymous

I sayed BEDS with an S, not BED :D LOL, I knew it you have interesting thoughts in your head :)

- anonymous

I got it from the relation tan^2(x) = sec^2(x) - 1.
∫tan^3(x)dx = ∫tan^2(x)*tan(x) dx = ∫(sec^2(x)-1)*tan(x) dx = ∫tan(x)sec^2(x) - tan(x) dx = ∫tan(x)sec^2(x) dx - ∫tan(x) dx. :P

- anonymous

nope :)

- anonymous

I never think of such things angoo =P

- anonymous

yes but quantum the question is :\[\int\limits_{}^{}tanx^3\]
and not :
\[\int\limits_{}^{}\tan^3x\]

- anonymous

hmm... well, I don't too, becouse things like those should be practice once married

- anonymous

I agree :)

- anonymous

quantum you copied the question wrong lol

- anonymous

good, smart girl, not the "new era" type

- anonymous

nah, I'm old fashioned ^_^ more classy

- anonymous

wonderful, smart, classy, what else could one want....

- anonymous

want what? ._.

- anonymous

Erm...alright, then we'll see when deidre clears it up. :P

- anonymous

like in, what else would I look for in a friend

- anonymous

lol , I agree Quantum

- anonymous

aww, angoo, you're soo sweet ^_^

- amistre64

im sticking with my safety net....(S) x^2 dx..... :)

- anonymous

not sweet, just relaxed and not trying to be someone I am not

- anonymous

lol amistre! and yes you are sweet andy ^_^

- anonymous

well, thanks, going to the dream world now, I think I will dream about beautiful land with happy little rabbits and dears and bears living together, and I will be ther too, we will play and have fun....

- anonymous

lala land, lol, I'm off to bed too, good night ^_^

- anonymous

and you are welcome :)

- anonymous

night night :)

- anonymous

sleep tight ~

- anonymous

:) I was about to say "don't let the bugs bite" but it is getting old, so..

- anonymous

lol, bye

- anonymous

bye

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