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<a https://www.thestudentroom.co.uk/showthread.php?t=7467335'> Year 12s: what will be the first way you research your future options? >>

FP2 Integral of arcoshx

I am currently unable to integrate arcoshx, could someone please help?

I started with:
u = arcoshx
du/dx = 1/ Square root(x^(2) -1)

But then get stuck as it would be the integral of: u du * (Square root(x^(2) -1))

Does anyone know where i went wrong and how to answer it?

Thanks
Reply 1
Avatar for M14B
M14B
18
Original post by Davi6336
I am currently unable to integrate arcoshx, could someone please help?

I started with:
u = arcoshx
du/dx = 1/ Square root(x^(2) -1)

But then get stuck as it would be the integral of: u du * (Square root(x^(2) -1))

Does anyone know where i went wrong and how to answer it?

Thanks


Integration by Parts I think
Reply 2
Avatar for Davi6336
Davi6336
OP
1
Original post by M14B
Integration by Parts I think


Alright sweet that worked, cheers
By parts, you should get x*arccosh(x) + (x+1)^1/2 * (x-1)^1/2 + C

A trivial lapsus of my memory, I shouldn't rush things.
(edited 8 years ago)
Original post by Davi6336
Alright sweet that worked, cheers


Not to be a buzzkill but I hope you understand why it worked, and the intuition behind finding that method. Many people don't.
Basically, if you can integrate xx times a function's derivative, then you can always integrate the function via IBP with 1 and the function itself.
Reply 5
Avatar for Zacken
Zacken
22
Original post by Bath~Student
By parts, you should get x*arccosh(x) + (1 - x^2)^1/2 + C


False.
Original post by Zacken
False.


Hilarious. You have quite the sense of humour.
Reply 7
Avatar for Zacken
Zacken
22
Original post by Bath~Student
Hilarious. You have quite the sense of humour.


No, it actually is false.
Original post by Zacken
No, it actually is false.


Fixed. Standard integrals and derivatives I memorise.. can happen.


I shall redeem myself before I turn to my homework: it is an endeavour far more important.
Reply 9
Avatar for Zacken
Zacken
22
Original post by Bath~Student
Fixed.


x+1x−1=x2−1\sqrt{x+1}\sqrt{x-1} = \sqrt{x^2-1}, by the way.
Original post by Zacken
x+1x−1=x2−1\sqrt{x+1}\sqrt{x-1} = \sqrt{x^2-1}, by the way.


Yes, and since RHS is prettier, why not keep it?

I am right in the fixed integral, am I not?

You are making me question reality. Perhaps my homework is what I should turn to..
Reply 11
Avatar for Zacken
Zacken
22
Original post by Bath~Student
I am right in the fixed integral, am I not?


Yes.
Original post by Zacken
Yes.


I can breathe again.
Reply 13
Avatar for Davi6336
Davi6336
OP
1
Original post by IrrationalRoot
Not to be a buzzkill but I hope you understand why it worked, and the intuition behind finding that method. Many people don't.
Basically, if you can integrate xx times a function's derivative, then you can always integrate the function via IBP with 1 and the function itself.


Oh ok i see that point, because then it means the second part (the integral) of the integration by parts formula can be integrated. Cheers
Reply 14
Avatar for Zacken
Zacken
22
Original post by Davi6336
Oh ok i see that point, because then it means the second part (the integral) of the integration by parts formula can be integrated. Cheers


Yep!

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