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A Level Maths Integration by Parts

I can get to the third line of the mark scheme, but don't know how to deal with the expressions and the powers of 2/3. How would you manipulate them so that things start to cancel out? So far I have [3/2(8)^2/3 x ln(8) - 9/4(8)^2/3] - [3/2(1)^2/3 x ln(1) - 9/4(1)^2/3] Thank you :smile:

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Reply 1
(I haven't bothered checking whether that's actually correct)
Let's simplify term by term.

- 8^(2/3) is just a number. I think it's 4? You can check on your calculator.
- ln(8) = ln(2^3) = 3ln(2)
- 1^blah = 1
- ln(1) = 0

Then hopefully things look nice.
Reply 2
Original post by cloudii
I can get to the third line of the mark scheme, but don't know how to deal with the expressions and the powers of 2/3. How would you manipulate them so that things start to cancel out? So far I have [3/2(8)^2/3 x ln(8) - 9/4(8)^2/3] - [3/2(1)^2/3 x ln(1) - 9/4(1)^2/3] Thank you :smile:


The power of 2/3 means square the cube root.

8^(2/3) = 4 does that help
Reply 3
Yes, thank you! I think I was just over-complicating it :smile:

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