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\[\large \int\limits_{0}^{x}t^2 \sqrt{2+5t^4})dt\] correct?

Yup, that's the integral we need to find

I was thinking fundamental theorem of calculus part 1 but that's more for derivative, hmm.

according to wolfram, this is not a simple integral

What's a simple integral? Is it still a simple integral without the boundaries (0 and x)?

it looks ugly either way

without limits
http://www.wolframalpha.com/input/?i=integral+%28t^2%29*sqrt%282%2B5t^4%29+dt

That is what I meant by not simple. I have no idea how to get that answer.

Yeah, I get the feeling that the real question was "Differentiate this with respect to x" haha

Opps there's a line between the x^5 and the bottom integral

you have and infty/infty so take the derivative of top and bottom

Oh good old L'Hopital's rule! Thank you so much!

Yeah that ^ hah

I am getting \( \sqrt{5} \)