# Calc II Integral

## 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!

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Mark44
Mentor

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