creativebuzz
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Which integration method should I use to integrate this?
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TeeEm
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(Original post by creativebuzz)
Which integration method should I use to integrate this?
square it out
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tiddlytom
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I'd be tempted to either expand it and do it, or notice that within the brackets is something like the formula for sinh(x).
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creativebuzz
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(Original post by tiddlytom)
I'd be tempted to either expand it and do it, or notice that within the brackets is something like the formula for sinh(x).
Ah got it, thanks!

Would you mind spotting where I went wrong in these two questions?

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creativebuzz
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(Original post by TeeEm)
square it out
Thank you!

What method would I use to integrate this two expressions?

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TeeEm
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(Original post by creativebuzz)
Thank you!

What method would I use to integrate this two expressions?

both require trig identities
First one is a bit hard
second is easy
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ghostwalker
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(Original post by creativebuzz)
...
f) Get the denominator in terms of tan's.

You can either do it by recognition
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- the from is f'(x)/f(x) -, or use a substitution let u="denominator"
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creativebuzz
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(Original post by TeeEm)
both require trig identities
First one is a bit hard
second is easy

As for the second one,

I used the trig equation tan^2x + 1 = cot^2x

and multiplied that by minus one ad changed the angle to 3x but doesn't that make you expression even more difficult?
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TeeEm
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(Original post by creativebuzz)
As for the second one,

I used the trig equation tan^2x + 1 = cot^2x WRONG

and multiplied that by minus one ad changed the angle to 3x but doesn't that make you expression even more difficult?
look at your identities

1 + cot2x = ....

that something (...) is a perfect differential
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creativebuzz
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(Original post by ghostwalker)
f) Get the denominator in terms of tan's.

You can either do it by recognition
Spoiler:
Show

- the from is f'(x)/f(x) -, or use a substitution let u="denominator"
I used the identity tan^2x + 1 = sec^2x

to get 2sec^2xtanx/2 + tan^2x

but I don't see how that is f'(x)/f(x)

because the integral of secxtanx is secx
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ghostwalker
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(Original post by creativebuzz)
I used the identity tan^2x + 1 = sec^2x

to get 2sec^2xtanx/2 + tan^2x

but I don't see how that is f'(x)/f(x)

because the integral of secxtanx is secx
What's the deriviative of 2+\tan^2x ?
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creativebuzz
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(Original post by ghostwalker)
What's the deriviative of 2+\tan^2x ?
I don't actually know.. :/
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ghostwalker
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(Original post by creativebuzz)
I don't actually know.. :/
Try a substitution, let u=tanx,

It's a specific example of the general form \displaystyle\dfrac{d}{dx}\Big((  f(x))^n\Big)=nf'(x)(f(x))^{n-1}

which you can also prove by using a substitution u=f(x)
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creativebuzz
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(Original post by TeeEm)
both require trig identities
First one is a bit hard
second is easy
I realised that I never finished working on question (f) and this time I took a different approach and I nearly got there except I can't seem to integrate (1 + sec^2x). (by the way, the last bit should be boxed not integrated because I already integrated it)



How would I take this further?
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