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# C4 integration

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1. Can anyone explain how to integrate sec^2(x)tanx ? thanks
2. (Original post by coconut64)
Can anyone explain how to integrate sec^2(x)tanx ? thanks
Note that the derivative of tanx is sec^2x, so you can apply the reverse chain rule

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3. (Original post by coconut64)
Can anyone explain how to integrate sec^2(x)tanx ? thanks
Think about what differentiates to give something that looks similar.
4. You could recognize that sec^2x is the derivative of tan x or use a u substitution, let u = tanx

(Original post by coconut64)
Can anyone explain how to integrate sec^2(x)tanx ? thanks
5. (Original post by NotNotBatman)
You could recognize that sec^2x is the derivative of tan x or use a u substitution, let u = tanx
I get how to obtain the sec^2x part but what about the tanx part? Also what about secx as this gives me secxtanx...

Thanks
6. (Original post by SeanFM)
Think about what differentiates to give something that looks similar.
I know that secx gives secxtanx but this doesn't give me sec^2 x though...

Thanks
7. (Original post by coconut64)
I get how to obtain the sec^2x part but what about the tanx part? Also what about secx as this gives me secxtanx...

Thanks
, so what does differentiating tan^2x result in?
8. (Original post by coconut64)
I know that secx gives secxtanx but this doesn't give me sec^2 x though...

Thanks
it's been given above, but it was tanx that you should be particularly interested in. It's worth looking at a list of all of those ones (sec, tan cosex, cot.. and what they differentiate to if you're stuck)
9. (Original post by coconut64)
I know that secx gives secxtanx but this doesn't give me sec^2 x though...

Thanks
(Original post by SeanFM)
it's been given above, but it was tanx that you should be particularly interested in. It's worth looking at a list of all of those ones (sec, tan cosex, cot.. and what they differentiate to if you're stuck)
Using the fact that differentiating sec x gives sec x tan x is an alternative to using the derivative of tan x.

I've always liked integrals that give you more than one answer and they look completely different at first sight (like sin x cos x)

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