# Integrating with radicals

1. Feb 25, 2013

### Cacophony

1. The problem statement, all variables and given/known data
for the following integrals, am I allowed to break them up like so:

1. ∫(1)/(sqrt(16-9x²)³) dx

= ∫(1)/(√16)³ · ∫(1)/(√-9x²)³ dx

2. ∫(x²)/(sqrt(x²-9)) dx

= ∫(x²)/(√x²) · ∫(x²)/(√-9) dx

3. ∫(1)/(x²(sqrt(a²+x²))) dx

= ∫(1)/(x²) · ∫(1)/(√a²) · ∫(1)/(√x²) dx

? ? ?

2. Relevant equations
none

3. The attempt at a solution
I need to know if I'm allowed to break them up like this before I start attempting a solution

2. Feb 25, 2013

### eumyang

Is this what you are writing for #1?
$\int \frac{1}{\left( \sqrt{16-9x^2}\right)^3} dx$
$=\int \frac{1}{\left( \sqrt{16}\right)^3} dx \cdot \int \frac{1}{\left( \sqrt{-9x^2}\right)^3} dx$
Yikes. No, you cannot do that!

$\sqrt{a - b} \ne \sqrt{a} \cdot \sqrt{-b}$
Better review the properties of radicals.

3. Feb 25, 2013

### Cacophony

Ok, guess i'll try something else. Thanks

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