# Thread: Intergration Problem - Square Roots?

1. ## Intergration Problem - Square Roots?

$\frac{3}{\sqrt{2t +1}}$

Can someone please explain how I do this. The square root on the bottom has really thrown me out. I can do them when there's no square root but because it's there I'm really not sure.

I was thinking,

$\frac{3}{2}$ $(2t+1)^{1/2}$

but yeah I'm not really sure.

Thanks!

2. Originally Posted by Kaynight
$\frac{3}{\sqrt{2t +1}}$

Can someone please explain how I do this. The square root on the bottom has really thrown me out. I can do them when there's no square root but because it's there I'm really not sure.

I was thinking,

$\frac{3}{2}$ $(2t+1)^{1/2}$

but yeah I'm not really sure.

Thanks!
Let

$\varphi=2t+1\Rightarrow{dt=\frac{1}{2}\varphi}$

So we have

$\frac{3}{2}\int\frac{d\varphi}{\sqrt{\varphi}}=3\s qrt{\varphi}$

Now back subbing we get

$3\sqrt{2t+1}$

3. Originally Posted by Kaynight
$\frac{3}{\sqrt{2t +1}}$

Can someone please explain how I do this. The square root on the bottom has really thrown me out. I can do them when there's no square root but because it's there I'm really not sure.

I was thinking,

$\frac{3}{2}$ $(2t+1)^{1/2}$

but yeah I'm not really sure.

Thanks!
Wrong, substitute $u = 2t+1, 3\int (2t+1)^{-\frac12}\, dt = 3 \int u^{-\frac12} \, \frac{du}2 = \frac32 \int u^{-\frac12} \, du = 3\sqrt{2t+1}$

4. Many thanks Isomorphism and Mathstud28!