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Integration

hey, need some help quickly, just switched from medicine to maths and am trying to revise maths, and got stuck.

How on earth to I integrate (x^2+a)^0.5. I could do ^-0.5, but not 0.5 :C Can someone help please?
Reply 1
Avatar for teily
teily
1
would u-substitution work? i haven't done maths in forever...
well i believe it would just be

(x2x^2 +a) ^3/2

then divided by 3/2
sw1208
hey, need some help quickly, just switched from medicine to maths and am trying to revise maths, and got stuck.

How on earth to I integrate (x^2+a)^0.5. I could do ^-0.5, but not 0.5 :C Can someone help please?


Neither of the above work as far as I remember, I'm pretty sure this is a messy one. I'd suggest doing it by parts so that you can exploit the fact you know how to do (x^2 + a)^(-0.5), although even that might get messy, I'll post some more in a moment.

Here's my attempts, I'll try split them up as hints, you should try before opening each new hint

Spoiler



This is a particularly messy way that I did at A-level, there might (edit:- The below should be easier really, though I'd never of thought of it a year ago for some reason) be a nicer way using the right substitutions, I'll try that now...

Spoiler

which can be solved by standard techniques.

This should work, I kind of rushed it.
Reply 4
Avatar for wizz_kid
wizz_kid
16
It is some long question : http://integrals.wolfram.com/index.jsp?expr=(x^2%2Ba)^0.5&random=false
Reply 5
Avatar for sw1208
sw1208
OP
oh seen so it's just a bare hard integral not that I couldnt do it. thanks x
sw1208
oh seen so it's just a bare hard integral not that I couldnt do it. thanks x

It's not actually that hard, it just takes a bit of patience.

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