# Thread: urgent help for calc 3

1. ## urgent help for calc 3

I don't get the first integral. How do they get to x(sqrt(x^2 + ^2 +1)? I would think you would need a ln.

2. shouldn't there be a 0.5(x(....) for the first integral?

3. The 0.5 gets cancelled out when you divide by the new power of 1/2.
$
\int \frac{xy}{\sqrt{x^2+y^2+1}}dy$

u = $x^2+y^2+1$
du = 2ydy
$
\int \frac {1}{2}x \frac {2ydy}{\sqrt{u}}$

$=\int \frac{1}{2}xu^{-1/2}du$
$=\frac {1}{2}x2u^{1/2}$
$x\sqrt{x^2+y^2+1}$