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please help with math (integrals)

category: general [glöplog]
please help. anyone is able to calculate (integral) of xcos(5x) dx ?
added on the 2005-01-27 17:13:33 by Chris_ZD Chris_ZD
6
(x/5)*sin(5x)+C
added on the 2005-01-27 17:34:39 by quisten quisten
1/25*cos(5*x)+1/5*x*sin(5*x)
added on the 2005-01-27 17:38:41 by Chris_ZD Chris_ZD
wow, you people actually know this!
added on the 2005-01-27 18:44:26 by skrebbel skrebbel
derive says:
COS(5·x)/25 + x·SIN(5·x)/5
added on the 2005-01-27 18:53:36 by Gargaj Gargaj
pi
added on the 2005-01-27 19:36:28 by sagacity sagacity
mmmmm pi
added on the 2005-01-27 19:36:48 by Gargaj Gargaj
oooh derive!! old good friend! :)
Alcohol and calculs don't mix. Never drink and derive!
added on the 2005-01-27 22:59:29 by chock chock
I demand a recount! =(
added on the 2005-01-27 23:16:04 by cerror cerror
null:
You need both partial integration and the substitution method for solving this task. If you want me to explain it in more detail, please ask me. Here's the way I solved it:

Formula of partial integration:
Int u(x) v'(x) dx = u(x) v(x) - Int u'(x) v(x) dx

I choose:
v'(x) := cos(5x)
=> v(x) = 1/5 sin(5x)

u(x) := x
=> u'(x) = 1

Using substitution method, we can transform:
Int cos(5x) dx = Int cos(z) dz
by defining z := 5x
=> z' = 5 = dx/dz
=> dz = dx / 5
From which follows (using the formula for Int cos(x) dz = sin(x)):
Int cos(z) dz = 1/5 sin(5x)

Let's insert this:
Int x cos(5x) = 1/5 x sin(5x) - 1/5 Int sin(5x) dx

In order to compute Int sin(5x) dx, we use the substitution method once again, and we get:
Int sin(5x) dx = -1/5 cos(x)

So we get:
1/5 x sin(5x) - 1/5 Int sin(5x) dx = 1/5 x sin(5x) + 1/25 cos(5x)

Quod erat demonstrandum.
added on the 2005-01-28 09:18:08 by Adok Adok
Choose life, choose Derive.
added on the 2005-01-28 11:35:32 by dixan dixan
Mathematica for life
added on the 2005-01-28 12:24:37 by rmeht rmeht
i chose not to choose life, i chose something else.
added on the 2005-01-28 12:26:04 by psenough psenough
i've chosen to love.
added on the 2005-01-28 13:04:12 by rmeht rmeht
adok, you are damn fucking complicated.
1) null already solved his/her own problem, see the 4th entry.
2) working method. first try: x*sin(5x). that doesn't work, but almost do; so let's try to correct it: x*sin(5x)/5 + cos(5x)/25. that's all.
3) choose washing machines, cars, compact disc players and a computer with some math software, but before that, learn some math yourself
added on the 2005-01-28 13:32:51 by blala blala
Damn, I should be studying now ;P
added on the 2005-01-28 13:34:14 by Optimus Optimus
blala: What I understood was that he didn't just need the solution, but the way of solving it.
added on the 2005-01-28 18:05:50 by Adok Adok
le compte est bon!
added on the 2005-01-28 19:38:49 by jb jb
adok: so you presented him an overcomplicated page-long argument, starting right with unmotivated "clever" choices - now he surely understand everything... if you want to teach, try instead to teach how to solve such problems in general. since general integration algorithms don't exist, i think the "try something which resembles what we want, and then try to gradually correct it" method is quite useful.
added on the 2005-01-28 20:10:39 by blala blala
It's simple, it's a formula which you memorize and use when it's appropriate. That's it.
added on the 2005-01-28 21:02:00 by Adok Adok
Memorizing formulas is generally a bad idea. The smart thing to do is to memorize and understand the ways to derive them. As an added bonus, you'll learn the formulas as well
added on the 2005-01-28 21:11:19 by Preacher Preacher

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