How do I go about this using u-substitution

Question

justjm · Answer

$\int_{ }^{ }x\sqrt{x+3}dx$

justjm · Answer

@Vocaloid @mhchen @Hero

myeyeshurt · Answer

Let u=x+3

justjm · Answer

I tried doing that but messed up but let me give it a try once again

justjm · Answer

thx for responding

myeyeshurt · Answer

You should get the (u-3)sqrt(u)=u^(3/2)-3sqrt(u) as the integrand

justjm · Answer

$$\int\limits_{}^{} x \sqrt{u} du$$
so now do I continue normally

myeyeshurt · Answer

Nah you're subbing wrong

justjm · Answer

Oh okay like this?

$$\int\limits_{}^{} (u-3) \sqrt{u} du$$

myeyeshurt · Answer

Yeah keep in mind that when you do u sub you need an expression for dx in terms of du

myeyeshurt · Answer

So here u=x+3 and du=dx

justjm · Answer

Yeah I did that
Since u=x+3
du/dx = 1
so du=dx

myeyeshurt · Answer

Yeah

myeyeshurt · Answer

Anyways you can distribute and integrate now

justjm · Answer

Thanks bro. So what you did is you had the u=x+3 but you changed the x from the integrand to u-3. Thanks. I was confused on how there was an x and a u.

myeyeshurt · Answer

Yeah these u sub integrals have a tendency to hide in plain sight. Trial and error is sometimes necessary

justjm · Answer

Ah okay. Thank you once again.