# Integrating tan2xWatch

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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?
0
12 years ago
#2

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

Would you integrate this in parts?

With and
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12 years ago
#3
You would use a substitution u = 2x.
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#4
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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12 years ago
#5
(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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#6
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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12 years ago
#7
(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)?
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12 years ago
#8
Or even .
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12 years ago
#9
I can't see how the "answer" is right then. Integrating tanx is ln secx.
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12 years ago
#10
The Edexcel formula book shows the integral of tan kx. Unfortunately, I've lost mine.
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12 years ago
#11
Derive it?

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12 years ago
#12
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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12 years ago
#13
I'd call easy, but, you know...
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4 years ago
#14
-1/2ln(cos2x)+c = 1/2ln((cos2x)^-1)+c = 1/2ln(1/cos2x)+c = 1/2lnsec2x +c
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4 years ago
#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...
1
4 years ago
#16
it seems nobody really made it clear
0
4 years ago
#17
(Original post by Supertangi)
it seems nobody really made it clear
you missed out those funny vertical brackets
0
4 years ago
#18
(Original post by the bear)
you missed out those funny vertical brackets
yep
seem so
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