What would the integral of a polynomial and a square root ( ex. (5x^4 -3) * sqrt(6x^2 + 10x) ) be? What method (usub, integration by parts, etc.) would you use to do this?

Question

mimi_x3 · Answer

Complete the square!

anonymous · Answer

BTW, the example i gave may not necessarily be solvable.. i just came up with a random one

mimi_x3 · Answer

Yeah, its solvable.
U substitution.

anonymous · Answer

what would you assign to u?

anonymous · Answer

Well, i mean, its hard to tell what method you wanna use, without a solid example, cause one problem, we can use various method, trig sub, inverse trig, hyperbolic, u-sub, things of that nature. And with this square root problem, sometime the integrals dont have elementary antideriaitves, so it could get really nasty

anonymous · Answer

would it be okay if I rase the whole thing to a power of 2, get a pretty long polynomial and then integrate it? 

@lagrangeson678, i gave a solid example, turns out it is solvable b/c the same question is in my testbook

anonymous · Answer

PLZ help?!

anonymous · Answer

the example problem you gave seems like it would be an integration by parts problem, i dont think just doing a straight up u-sub would solve this. Using integration by parts follows LIPET for choosing its u in many cases

mr.math · Answer

I can't say there's one method that would solve any problem with your description. Practice would help you determine which method to pick. But I can say they are usually solved using substitution.

anonymous · Answer

Most of integration comes with practice and knowing what forms to looks for and/or ways that you can manipulate the equation to look like how you want it to be so that you are able to integrate it

anonymous · Answer

According to LIPET, you would choose the 5x^4 -3 for u, right? then, du is 20x^3, dv is sqrt(6x^2 + 10x) and v would be (6x^2 + 10x) ^ 3/2 all divided by 6x +5

and then just plug into uv - fvdu?

anonymous · Answer

yes, in this case you may need to do integration by parts multiple times, for the example problem it looks like you would have to take by parts about 5 times or so

anonymous · Answer

okay thanks, so tabular method would be easier then if it is multiple step?

anonymous · Answer

yes