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# ∫ (sec x)(sec x)(tan x) Tweet

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1. ∫ (sec x)(sec x)(tan x)
∫ (sec x)(tan x) = sec x
so isn't ∫ (sec x)(sec x)(tan x) = ∫(sec x)(tan x) x ∫(sec x) ?
2. Re: ∫ (sec x)(sec x)(tan x)
No.

3. Re: ∫ (sec x)(sec x)(tan x)
(Original post by sabre2th1)
∫ (sec x)(tan x) = sec x
so isn't ∫ (sec x)(sec x)(tan x) = ∫(sec x)(tan x) x ∫(sec x) ?
You can't do that with integrals. In general:

4. Re: ∫ (sec x)(sec x)(tan x)
(Original post by SecondHand)
No.

(Original post by notnek)
You can't do that with integrals. In general:

Ah.. I see. I am still confused on how:

∫[(2sec x)(sec x)(tan x)] = sec2x

Thanks
5. Re: ∫ (sec x)(sec x)(tan x)
(Original post by sabre2th1)
Ah.. I see. I am still confused on how:

∫[(2sec x)(sec x)(tan x)] = sec2x

Thanks
What's the differential of tanx? Now look at the differential of tan^2 x
6. Re: ∫ (sec x)(sec x)(tan x)
(Original post by sabre2th1)
Ah.. I see. I am still confused on how:

∫[(2sec x)(sec x)(tan x)] = sec2x

Thanks
Its an integral of the form

For such integrals we try differentiating,

Spoiler:
Show

7. Re: ∫ (sec x)(sec x)(tan x)
(Original post by sabre2th1)
Ah.. I see. I am still confused on how:

∫[(2sec x)(sec x)(tan x)] = sec2x

Thanks
You've been given two different right answers to your question. Differentiate either sec^(x) or tan^2(x) using the chain rule and you get the integrand you started with. You might reasonably ask 'which is it, then?'

When you integrate you introduce an arbitrary constant. What's the difference between sec^2(x) and tan^2(x)?
8. Re: ∫ (sec x)(sec x)(tan x)
(Original post by cpdavis)
What's the differential of tanx? Now look at the differential of tan^2 x

(Original post by raheem94)
Its an integral of the form

For such integrals we try differentiating,

Spoiler:
Show

(Original post by ian.slater)
You've been given two different right answers to your question. Differentiate either sec^(x) or tan^2(x) using the chain rule and you get the integrand you started with. You might reasonably ask 'which is it, then?'

When you integrate you introduce an arbitrary constant. What's the difference between sec^2(x) and tan^2(x)?
I've got it thanks alot !
9. Re: ∫ (sec x)(sec x)(tan x)
(Original post by raheem94)
Its an integral of the form

For such integrals we try differentiating,

Spoiler:
Show

If you have ∫(sec2x)(tan2x), then how do you determine which [of (sec2x) and (tan2x)] is the f(x) and which is the f'(x)?
10. Re: ∫ (sec x)(sec x)(tan x)
(Original post by sabre2th1)
If you have ∫(sec2x)(tan2x), then how do you determine which [of (sec2x) and (tan2x)] is the f(x) and which is the f'(x)?
I've tried it both ways, and only one works.
11. Re: ∫ (sec x)(sec x)(tan x)
(Original post by ian.slater)
I've tried it both ways, and only one works.

Given that

Divide both side by