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#
integrate (x/(1+3x)^4) dx
hmm seperate the x and (1+3x)^(-4) terms then integrate by parts.
There will be a trig substitution for 1/(1+3x) iirc
a^2+u^2 substitute u=a*tan(theta), where a=1 and u=sqrt(3x), that 4th power bit will probably come in handy but its a nasty problem (I hate integration by substitution).
Giving, 1/((1+3x)^4)=1/(a*tan(theta))^4,
I hope this helps :)
(emptyspace, Thu 12 Dec 2013, 11:42, archived)
# my brain just liquefied and leaked out of my ears
(I helped save b3ta! PedroHin Come along & ride on a Flantastic Voyage, Thu 12 Dec 2013, 11:46, archived)
# hehe
That happened to me months ago....bleurgh
(emptyspace, Thu 12 Dec 2013, 11:52, archived)
#
My cats breath smells of cat food...
(robneymcplum spiced up his life on, Thu 12 Dec 2013, 11:54, archived)
# This is my sandbox. I'm not allowed to go in the deep end.
(I helped save b3ta! da5id <YOUR SIG HERE>, Thu 12 Dec 2013, 12:05, archived)
# 'don't you see Bart, rdr^2?'
rdrr
(emptyspace, Thu 12 Dec 2013, 12:11, archived)
# Oohh dear
Weird how the simple looking ones are a bitch to do...

Ta!
(smellysamlyingcable Seaman on, Thu 12 Dec 2013, 12:03, archived)
#
Just realised that,
x=1/3(tan(theta))^2,
so there should be some nice cancelations to make!
(emptyspace, Thu 12 Dec 2013, 12:10, archived)
# Like this?
(smellysamlyingcable Seaman on, Thu 12 Dec 2013, 15:47, archived)
# WTF!
Never posted such a big picture...
Must be important.
(smellysamlyingcable Seaman on, Thu 12 Dec 2013, 15:47, archived)
# Looks like winner!
Have a celebratory woo
(emptyspace, Thu 12 Dec 2013, 15:55, archived)
# But but but
is that thing I did with the "t" to find the "x" legal? I was totally ad-libing there...
(smellysamlyingcable Seaman on, Thu 12 Dec 2013, 17:17, archived)
# seems ok as you did define x, t, dx, dt, might be worth showing dx/dt or dt/dx to show how you got dx & dt though...
As far as I can see your equals signs hold everywhere which means it must be true! If the question didn't demand a specific substitution you should be fine. Merry Christams and good luck, also what is your field of study?
(emptyspace, Thu 12 Dec 2013, 18:02, archived)
# Engineering watch officer
Aka officer that's a mechanic on-board big ships (500 tons up).
Started last year. Passed all my exams except maths...
So I'm on the lookout for math trickery involving integrals and derivatives.
(smellysamlyingcable Seaman on, Thu 12 Dec 2013, 18:06, archived)
# And trigonemetry
But the calculus kind...
Cos(x)^3=cos(1-sin(x)^2) mumbo jumbo.
I'm so shit at trigo...
That's why I do thermodynamics and no map reading.
(smellysamlyingcable Seaman on, Thu 12 Dec 2013, 18:17, archived)
# Trig is a bastard, it's worth knowing the complex exponential forms of sine and cosine as you can then avoid trying to remember the identities.
ie.
sin(x)=1/(2i)(e^(ix)-e^(-ix))
and,
cos(x)=1/2(e^(ix)+e^(-ix)
where,
i=sqrt(-1) (you might know 'i' as 'j')
Other than that I can only tell you the trick to learning maths is do lots of problems,
until your sick of em...
and then do some more.
Good luck with your studies :D
(emptyspace, Thu 12 Dec 2013, 20:34, archived)