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# C4 Integration watch

1. I think integration is a decent topic but I have no idea how to integrate the following:

• 4Cos3xSin2x
• Sec2xtan2x

Guides on how to integrate these would be greatly appreciated,

Thanks
2. (Original post by Leking9)
I think integration is a decent topic but I have no idea how to integrate the following:

• 4Cos3xSin2x
• Sec2xtan2x

Guides on how to integrate these would be greatly appreciated,

Thanks
Do you know how to integrate CosxSinnx
3. (Original post by Leking9)
I think integration is a decent topic but I have no idea how to integrate the following:

• 4Cos3xSin2x
• Sec2xtan2x

Guides on how to integrate these would be greatly appreciated,

Thanks
For the second one recall what the differential of Tanx is
4. (Original post by TenOfThem)
Do you know how to integrate CosxSinnx
Not really, the only way I know is to do it by parts but that's extremely long
5. (Original post by TenOfThem)
For the second one recall what the differential of Tanx is

sec2​x
6. (Original post by Leking9)
Not really, the only way I know is to do it by parts but that's extremely long

(Original post by Leking9)
sec2​x

Have you done inverse chain rule .... If so these are both easy

If not substitution ... U=sinx and u=tanx
7. (Original post by TenOfThem)
Have you done inverse chain rule .... If so these are both easy

If not substitution ... U=sinx and u=tanx

"Inverse chain rule" I've been taught according to what's inside the C4 edexcel book and for some reason I can't see any exercises on it nor has my teacher gone over it
8. (Original post by Leking9)
"Inverse chain rule" I've been taught according to what's inside the C4 edexcel book and for some reason I can't see any exercises on it nor has my teacher gone over it
It is not called that in the book

It is just by recognition

If you know what sinx differentiates to, then you know what (sinx)^n differentiates to

Therefore you can integrate cosx (sinx)^n

Or use the substitutions that I pointed out
9. (Original post by Leking9)
"Inverse chain rule" I've been taught according to what's inside the C4 edexcel book and for some reason I can't see any exercises on it nor has my teacher gone over it
It's called integration by parts and you definitely should have covered it?
10. (Original post by TVIO)
It's called integration by parts and you definitely should have covered it?
These questions do not require IBP
11. (Original post by Leking9)
"Inverse chain rule" I've been taught according to what's inside the C4 edexcel book and for some reason I can't see any exercises on it nor has my teacher gone over it
It's noting that the form of the integral is in , and answering the question via recognition. In reality it's just a simple substitution, but with time you'll be able to do them by recognition.

Thus the integral becomes:

12. (Original post by TenOfThem)
These questions do not require IBP
could use sin(a+-b) formulas

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13. (Original post by physicsmaths)
could use sin(a+-b) formulas

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Could you?

Since both of these integrals are very straightforward I would be wary of introducing anything new
14. (Original post by TenOfThem)
Could you?

Since both of these integrals are very straightforward I would be wary of introducing anything new
That's how I always done the sinnxcosmx ones. It's just using the trig formulas to cancel into a very simple integral.

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15. 4cos(3x)sin(2x)= 2sin(5x) -2sinx

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16. (Original post by physicsmaths)
That's how I always done the sinnxcosmx ones. It's just using the trig formulas to cancel into a very simple integral.

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Those questions .... Yes

Not the ones in the OP though
17. (Original post by TenOfThem)
Those questions .... Yes

Not the ones in the OP though
Oh, is that raised to the power 3? I thought it was cos(3x)sin(2x)

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