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# C4 Integration with Trig Identities watch

1. I'm stuck on the following question:

Find the following integrals:
c) sec^2 2x (1+sin2x) dx
= (sec^2 2x + sec^2 2x sin2x) dx
= (sec^2 2x + sec2x tan2x) dx
= 0.5tan2x + 0.5sec2x + C

The problem I have is I don't understand how I'm supposed to get from sec^2 2x sin2x to sec2x tan2x
The question is here if it's easier to read

https://e1934e482e1b0d2c8580c3a986eb...EZ3UTQ/CH6.pdf

Exercise B Question 2c
2. (Original post by JW22)
I'm stuck on the following question:

Find the following integrals:
c) sec^2 2x (1+sin2x) dx
= (sec^2 2x + sec^2 2x sin2x) dx
= (sec^2 2x + sec2x tan2x) dx
= 0.5tan2x + 0.5sec2x + C

The problem I have is I don't understand how I'm supposed to get from sec^2 2x sin2x to sec2x tan2x
The question is here if it's easier to read

https://e1934e482e1b0d2c8580c3a986eb...EZ3UTQ/CH6.pdf

Exercise B Question 2c

So

Now use the fact that and
3. (Original post by JW22)
I'm stuck on the following question:

Find the following integrals:
c) sec^2 2x (1+sin2x) dx
= (sec^2 2x + sec^2 2x sin2x) dx
= (sec^2 2x + sec2x tan2x) dx
= 0.5tan2x + 0.5sec2x + C

The problem I have is I don't understand how I'm supposed to get from sec^2 2x sin2x to sec2x tan2x
The question is here if it's easier to read

https://e1934e482e1b0d2c8580c3a986eb...EZ3UTQ/CH6.pdf

Exercise B Question 2c
For the first one split the fraction up into 2 separate fractions. Each of these fractions can then be integrated just by considering standard results.
4. integrate cosec^22xcot2x (cosec squared 2x multiplied by cotx)
If you have the c4 book it's Ex 6E Q2b

I'M VERY VERY CONFUSED
5. (Original post by habzi)
integrate cosec^22xcot2x (cosec squared 2x multiplied by cotx)
If you have the c4 book it's Ex 6E Q2b

I'M VERY VERY CONFUSED
Try u = cosec^2 2x.
6. (Original post by Zacken)
Try u = cosec^2 2x.
substitution method right?
I did and for some reason I can't get to the answer! *help*
7. (Original post by habzi)
I did and for some reason I can't get to the answer! *help*
I think Zacken meant u = cosec2x
8. (Original post by habzi)
substitution method right?
I did and for some reason I can't get to the answer! *help*
(Original post by TeeEm)
I think Zacken meant u = cosec2x
Nope, u = cosec^2 2x, since du/dx = -4 cot 2x cosec^2 2x which cancels nicely in the integrand.
9. (Original post by Zacken)
Nope, u = cosec^2 2x, since du/dx = -4 cot 2x cosec^2 2x which cancels nicely in the integrand.
I am sorry about my limitations ...
10. but the answer is supposedly -1/4cot^2 2x
11. (Original post by habzi)
but the answer is supposedly -1/4cot^2 2x
Yes, I get that too! Why don't you post a new thread, tag me on it and put up a picture of your working so I can see where you're going wrong?
12. (Original post by habzi)
integrate cosec^22xcot2x (cosec squared 2x multiplied by cotx)
if you have the c4 book it's ex 6e q2b

i'm very very confused
what is this omfg it looks like a massive leap from AS 😔😁
13. (Original post by RueXO)
what is this omfg it looks like a massive leap from AS 😔😁
Spoiler:
Show
It's not a huge leap, dw
14. (Original post by RueXO)
what is this omfg it looks like a massive leap from AS 😔😁
As above, refrain from necroposting. :-)

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