# Integrals - first by substitution then by parts

• May 17th 2006, 06:29 PM
dsspence
Integrals - first by substitution then by parts
we're given the integral 2cos(ln(x))dx

and told to first use substitution then integration by parts, could someone kindly point me in the right direction
• May 17th 2006, 06:48 PM
ticbol
Quote:

Originally Posted by dsspence
we're given the integral 2cos(ln(x))dx

and told to first use substitution then integration by parts, could someone kindly point me in the right direction

Right direction?
Okay, go to the Calculus thread in this forum, look for the posting by nirva, "Some calc questions". Open that. The second problem there is almost the same as yours, except that yours has "2" before the cos(ln(x)).
If you know what to do with that "2", and you could follow the solution there of that second problem, then you should be able to get your integral.
• May 17th 2006, 06:50 PM
ThePerfectHacker
Quote:

Originally Posted by dsspence
we're given the integral 2cos(ln(x))dx

and told to first use substitution then integration by parts, could someone kindly point me in the right direction

You have,
$\displaystyle \int \cos (\ln x) dx=\int \frac{x\cos (\ln x)}{x}$
Use substitution $\displaystyle u=\ln x$ then, $\displaystyle u'=1/x$ and $\displaystyle x=e^u$
Thus,
$\displaystyle \int e^u \cos u \frac{du}{dx} dx=\int e^u \cos u du$

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I am going to stop here because I realized that ticbol made a post before me and already answered this question. Do as he says.