higher maths question im stuck at

[jp_2031]

okay i know how to intergrate normal equations , but what is the equation is like this:
intergrate
dx
----
2x�

also this one
intergrate ( x� - 1 ) dx
...........................---
.............................x�

sorry it wouldnt let me use spaces so i used .'s lol Please note im not asking you to do my homework or to work these out, i only want to know how to do them as they are frying my brain.
Thanks.

[Peter Pedant]

HI

I will do part 2 as that is more straightforward

divide through by x2

and you get 1 - x^-2

The integral of this is straightforwrad ie x + x -1

That is integration by standard rules - just as you inntergrate x3 by jacking up the index x4 and then dividing by the reciprocal of the index, toget 1/4 x ^ 4
The only whole nuber indec this does not work for is 1/x whose inntergral is log x

[Peter Pedant]

OK Part 1 - I think the same rules apply to fractional indices

so this is 1/2 x ^-1/2

and so add one to the inndex and fiddle around with the constant in the normal way and you get

x^1/2

differentitate to do the check , and you get 1/2 x ^ -1/2

So when you get back to Math class
ask the teacher ifthe rule applies to all fractional indices

is what is the integral of x to the power 5/6

and then follow that up with,
what about x to the power of root 2 ?
(yeah you read right not x to the 2 but x to the root 2)