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Calc II Integral

  • #1

Homework Statement



Indefinite integral of (x^2+5x+16)/sqrt(x^2-16x)

Homework Equations



Trig substitution and identities.


The Attempt at a Solution



I've tried setting x = 4 sec x but it has turned into a mess, and I really don't know where to go now. Using x, I'm left with

(16sec^2(x)+20sec(x)+64sec(x)tan(x))/sqrt(16sec^2(x)-64sec(x))

But I'm not even sure if I've done this right. Any help would be much appreciated! Thanks!
 

Answers and Replies

  • #2
33,506
5,192

Homework Statement



Indefinite integral of (x^2+5x+16)/sqrt(x^2-16x)

Homework Equations



Trig substitution and identities.


The Attempt at a Solution



I've tried setting x = 4 sec x but it has turned into a mess, and I really don't know where to go now. Using x, I'm left with

(16sec^2(x)+20sec(x)+64sec(x)tan(x))/sqrt(16sec^2(x)-64sec(x))

But I'm not even sure if I've done this right. Any help would be much appreciated! Thanks!
You probably did your trig substitution too soon.

For the expression in the radical, complete the square to get x2 - 16x + 64 - 64. This factors into (x - 8)2 - 64, which you can turn into u2 - 82.
 
Last edited:
  • #3
hunt_mat
Homework Helper
1,739
18
I would work on the denominator first, so:
[tex]
\sqrt{x^{2}-16x}=\sqrt{(x-8)^{2}-64}
[/tex]
and then let:
[tex]
x=8+8\cosh u
[/tex]
 

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