Find the integral of:

$$\int\limits_{}^{} t \sqrt{4+9t^2 + 16t^4}$$

Question

Find the integral of:

$$\int\limits_{}^{} t \sqrt{4+9t^2 + 16t^4}$$

anonymous · Answer

$$\int\limits_{}^{} t \sqrt{4+9t^2 + 16t^4}$$

anonymous · Answer

Not sure if a u-substitution will work, might need to do integration by parts.

anonymous · Answer

ok, let me try it by parts.

anonymous · Answer

Alright, so if I was going to do this by parts, how would I split it?

anonymous · Answer

I would take u=t and dv=the rest : du=dt

anonymous · Answer

Im thinking 

$$u = \sqrt{4+9t^2} and  dv = \sqrt{16t^4}$$

anonymous · Answer

doesn't seem right

anonymous · Answer

No, you can't split up a radical like that.

anonymous · Answer

How can I integrate that dt then? Doesn't seem to make it easier.

anonymous · Answer

It looks like along the way during integration-by-parts you can do a u-sub. (or maybe a w-sub, since 'u' has already been used).

anonymous · Answer

Grr, I just wrote a bunch of equations then my browser crashed..
I'll try going through it another way and let you know if it's any easier.

anonymous · Answer

ok, thanks