# c4 integration questionWatch

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#1
Step by step, could somebody break down how to integrate Sec^2(2x)tan^2(2x)

If the solution requires integration by parts or substitution, please explain why you chose that method over the other.

The answer in the mark scheme is 1/6 * tan^3(2x)

thank you!
0
2 years ago
#2
Try using the substitution . (the rest should be relatively straightforward)

Why would I use this method? Because the substitution sticks out at me. (also quicker and less messy)
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2 years ago
#3
i would notice that if you write this as sec^2(2x) (tan(2x))^2, then the first part is the bit in the bracket in the second part differentiated (up to a constant). This means that you can do it by inspection (sometimes called the reverse chain rule in this case).

If you want to do it formally, use the substitution u = tan(2x).

I'm afraid that the best answer I can give to "why this way?" is experience. When you do a lot of these, you'll start to notice the patterns, and the ones that come up often.
2
#4
Got it, thanks

Actually guys, I'm still struggling, this is for only 3/75 marks so I don't think a long solution is the right way. It's CCEA exam board and they may have made a mistake. I've checked the formula sheet and only the tan to sec^2x when differentiated identity is provided. Please help!

Integration by Inspection is not on the specification, but I will learn it anyway for these sticky situations
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2 years ago
#5
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2 years ago
#6
(Original post by Young Jimmy)
Got it, thanks

Actually guys, I'm still struggling, this is for only 3/75 marks so I don't think a long solution is the right way. It's CCEA exam board and they may have made a mistake. I've checked the formula sheet and only the tan to sec^2x when differentiated identity is provided. Please help!

Integration by Inspection is not on the specification, but I will learn it anyway for these sticky situations
Start by differentiating your substitution to obtain an expression for in terms of , and then adapt the integrand appropriately. You should be left with an integral that will look nice and familiar Note that , as should be in your formula booklet.
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