Calc II Integral Homework Solving Attempts

[sydneyfranke]

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!

 

[Mark44]

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.

 

[hunt_mat]

I would work on the denominator first, so:
$$\sqrt{x^{2}-16x}=\sqrt{(x-8)^{2}-64}$$
and then let:
$$x=8+8\cosh u$$