integrating cos or sin (lnx) Watch

gyrase
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#21
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#21
(Original post by AlphaNumeric)
Whenever I see an 'integrate cos....' question I instantly think about it's exponential form or taking the real or imaginary parts of e^{i....}
How would you integrate excos(x) with respect to x, using your method?

Edit; Never mind, got it. Nice method indeed.
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arktos
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#22
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(Original post by sebbie)
So in Year 13, upon seeing such a question you would have known to use such a method? Does it come up in Further Maths, AEA is meant to be done with only C1-C4 knowledge...

Does parts work for something like cos (lnx) as i thought parts only worked when it was two products....
Sebbie, he used parts because using the substitution u=lnx:

du/dx =1/x x=e^u
dx = x.du = e^u du

forms a product integral e^u cos[u] du.

Alpha, is that degree maths, or have a missed a lesson?
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AlphaNumeric
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#23
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I'd say if you were very comfortable with complex numbers, then it's A Level. If you're not too familiar with them, then it's 1st year degree.

Actually justifying that \ln(z^{i}) = i \ln z, as DDCA points out, is probably second year degree material, perhaps even third, but suffice for A Level you don't know a proof from your elbow so just ignore the question of "Can I do this?"
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