Integral cos (ln 6x) dx ... please help!
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Integral cos (ln 6x) dx ... please help!

[From: ] [author: ] [Date: 11-08-05] [Hit: ]
so dw = (1/x) dx....The x in xdw is a problem.rewrite as w = log (base e) 6x.......
this problem is under the integration by parts section in my book ... but im stuck and really don't know where to start.

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This one is hard to explain over a computer, however, I will try.
It involves substituting prior to integration by parts.

Start by letting w = ln(6x), so dw = (1/x) dx.... xdw = dx
The x in xdw is a problem. We go back to w = ln(6x)
rewrite as w = log (base e) 6x...
The w is now the exponent that goes on the e to equal 6x
e^w = 6x
(1/6) e^w = x
instead of xdw = dx.... (1/6) (e^w)dw = dx

your integral becomes (1/6) (e^w)cos(w)dw

let u = e^w and dv = cos(w) dw

Go to Work!

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w = ln 6x ---> dw = dx / x...but x = (1/6) e^w---> (1/6) e^w cos w dw..now IBP
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