2007-01-26 23:37:07 · 3 answers · asked by aditi 1 in Science & Mathematics ➔ Mathematics
As was said, when n=1 it is a logarithm. When n=2 it is arctanx.
When n=3 you have to factor the denominator into (x+1)(x^2-x+1), break up fraction using partial fractions and integrate each term. The first part is a constant times ln(x+1). In the second part you complete the square, break up the parts and get a log and an arctan.
For n in general, you factor it into quadratics which in this case has to do with the roots of unity, and then complete their squares and get a logarithm and an arctan for each quadratic.
2007-01-29 15:58:11 · answer #1 · answered by berkeleychocolate 5 · 0⤊ 0⤋
[x(1+n)+x^(n+1)] /(n+1)
2007-01-27 08:08:47 · answer #2 · answered by Paul B 3 · 0⤊ 0⤋
Actually the value of the integral depends on the value of n.if n=1,the value is log(1+x).
2007-01-27 07:41:12 · answer #3 · answered by sanna kumar 1 · 0⤊ 0⤋