King of TSR
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#1
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#1
Hi all
How do you integrate tan2x, since the answer is meant to be 1/2 sec2x + c, but im sure it must involve ln(...) no?
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Totally Tom
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#2
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#2
 tan2x=\frac{2tanx}{1-tan^2x}

Hmmm, I don't know, haven't done much trig calculus if any at all.

Would you integrate this in parts?

With \frac{1}{1-tan^2x} and  2tanx
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Dystopia
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#3
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You would use a substitution u = 2x.
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King of TSR
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#4
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nope, the simple way is to rewrite tan2x as sin2x/cos2x - then integrate by substitution. I get the answer as -1/2 ln(cos2x) + c. How can you manipulate this to equal 1/2 ln(secx) +c ????
Thanks
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Dystopia
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#5
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(Original post by The Philosopher)
nope, the simple way is to rewrite tan2x as sin2x/cos2x - then integrate by substitution. I get the answer as -1/2 ln(cos2x) + c. How can you manipulate this to equal 1/2 ln(secx) +c ????
Thanks
Log laws. But it would be 2x, not x.
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King of TSR
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#6
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Hmm in the text book it says x - thats what was confusing me!
Please could you run through it step by step (the log laws bit)?
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Dystopia
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#7
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(Original post by The Philosopher)
Hmm in the text book it says x - thats what was confusing me!
Please could you run through it step by step (the log laws bit)?
a \log(x) = \log(x^{a})
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DFranklin
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#8
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Or even \log x = - \log(1/x).
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Fointy
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#9
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I can't see how the "answer" is right then. Integrating tanx is ln secx.
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Swayum
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#10
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#10
The Edexcel formula book shows the integral of tan kx. Unfortunately, I've lost mine.
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calcium878
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#11
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Derive it?

\int \tan(kx)\text{d}x = \frac{1}{k}ln|\sec(kx)| + c
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*Sparkle*
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#12
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I'm pretty sure that's in the formula book...I've forgotten everything mathsy, but remember that being one of the simplest integrations.
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calcium878
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#13
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I'd call \int \cos{x} \text{d}x = \sin{x} + c easy, but, you know...:p:
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Supertangi
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#14
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-1/2ln(cos2x)+c = 1/2ln((cos2x)^-1)+c = 1/2ln(1/cos2x)+c = 1/2lnsec2x +c
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DFranklin
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#15
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#15
(Original post by Supertangi)
-1/2ln(cos2x)+c = 1/2ln((cos2x)^-1)+c = 1/2ln(1/cos2x)+c = 1/2lnsec2x +c
You're replying to an 8 year old post...
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Supertangi
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#16
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it seems nobody really made it clear
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the bear
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#17
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(Original post by Supertangi)
it seems nobody really made it clear
you missed out those funny vertical brackets
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Supertangi
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#18
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(Original post by the bear)
you missed out those funny vertical brackets
yep
seem so
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