Integration problem?

0 ⤊

Integration problem?

How do you integrate this (4x^2)/[(1+x^2)^2]?
Any help pls? Thanks!

2006-09-28 22:47:28 · 2 answers · asked by sky_blue 1 in Science & Mathematics ➔ Mathematics

2 answers

(4x^2)/[(1+x^2)^2]
=2(x^2+1)/[(1+x^2)^2]
+2(x^2-1)/[(1+x^2)^2]
=2/(1+x^2)
+2(x^2-1)/[(1+x^2)^2]
==>
int((4x^2)/[(1+x^2)^2])
=int(2/(1+x^2))
+int(2(x^2-1)/[(1+x^2)^2])
=2arctan(x)
-2x/(x^2+1)

2006-09-29 00:05:27 · answer #1 · answered by Mamad 3 · 0⤊ 0⤋

(4x^2)[(1+x^2)^2)
4x^2(1+2x^2+x^4)
4x^2+8x^4+4x^6
now integrate term by term:
4/3 x^3 + 8/5 x^5 + 4/7 x^7

2006-10-02 23:23:38 · answer #2 · answered by yupchagee 7 · 0⤊ 0⤋