how to integrate 2t[(2+4t^2)^1/2] dt?

Question

amorfide · Answer

you will have to use integration by parts I believe

irishboy123 · Answer

nah.  **differentiate** (2+4t^2)^3/2 and see what you get.  work from there.

amorfide · Answer

$$\int\limits_{a}^{b}u(t)v'(t)=u(t)v(t) - \int\limits_{a}^{b}u'(t)v(t)$$

anonymous · Answer

Thanks amorfide. I'll try that.

anonymous · Answer

is there anyway to check if my answer was right?

welshfella · Answer

yes  differentiate your answer to see if it comes back to the function in the question

anonymous · Answer

how do u choose which one is u and v?

welshfella · Answer

thats a good question - you want to make the integration u'(t)v(t) relatively easy

welshfella · Answer

welshfella · Answer

maybe you have the question wrong?

phi · Answer

I would let
$$ u = 4t^2+2 \ du = 8t~ dt $$

welshfella · Answer

yes  that substitution seems promising

phi · Answer

thus
$$ dt = \frac{du}{8t} $$
use that and u in your original equation

welshfella · Answer

you would have to convert 2t to an expression in u

welshfella · Answer

- no maybe not

welshfella · Answer

the 2t would cancel out

anonymous · Answer

i found it! Thanks so much phi! Will give u a medal xD

welshfella · Answer

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