INDEfInite INtegration-pls help

ca anyone pls help me out.........?

the integral *heavily* depends on what n is.

Case 1: n = 0.

Integral (1/(1 + 0) dx) = Integral (1)dx = x + C

Case 2: n = 1:

Integral (1 / (1 + x)) dx = ln |1 + x| + C

Case 3: n = 2:

Integral (1 / (1 + x^2)) dx = arctan(x) + C

Case 4: n = 3:

Integral (1 / (1 + x^3)) dx, and this may not even be expressable in terms of elementary functions.

How about if n = -1? Then

Integral (1 / (1 + x^(-1))dx = Integral (x / (x + 1)) dx
= Integral (1/(x + 1) + 1) dx
= ln|x + 1| + x + C

Let's see what happens if n = -2:

Integral (1 / (1 + x^(-2)) ) dx =
Integral ( (x^2) / (x^2 + 1) ) dx =
Integral ( [1 / (x^2 + 1)] + 1 ) dx =

arctan(x) + x + C

Then there are the fractional cases, like n = 1/2, 1/3, etc... which, also, may not be expressable as elementary functions.

The bottom line is that, without great difficulty, there is no way to find a general formula for the integral of (1 / (1 + x^n)).

ok then pls integrate

∫1/1+x^16