Question

Find the integral of:

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

Answer 1

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

Answer 2

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

Answer 3

ok, let me try it by parts.

Answer 4

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

Answer 5

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

Answer 6

Im thinking

\[u = \sqrt{4+9t^2} and dv = \sqrt{16t^4}\]

Answer 7

doesn't seem right

Answer 8

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

Answer 9

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

Answer 10

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).

Answer 11

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.

Answer 12

ok, thanks