integral of..?

5 ⤊

x/(1+x^2)^2

2006-08-15 10:00:17 · 3 answers · asked by Les L 1 in Science & Mathematics ➔ Mathematics

3 answers

- 1 / 2(1 + x^2) + C

2006-08-19 02:33:59 · answer #1 · answered by Joe Mkt 3 · 2⤊ 0⤋

If u = 1 + x^2, the denominator is u^2 and the numerator is half of the derivative of u. Therefore,

INT x / (1+x^2)^2 dx
=
1/2 INT du / u^2
=
-1/2 * (1/u + C)
=
-1/[2 + 2x^2] + C

2006-08-15 17:07:37 · answer #2 · answered by dutch_prof 4 · 2⤊ 1⤋

Integral of { x / (1+x^2)^2 dx}

define u = 1 + x^2 ; then du = 2x dx and dx = du / 2x

Now, replace everything:

Integral of { x / (1+x^2)^2 dx}
= Integral of { x / (u)^2 du / 2x}
= Integral of { x/2x * 1/(u)^2 * du}
= Integral of { 1/2 * 1/(u)^2 * du}
= -(1/2u) + C
= -(1 / 2(1 + x^2)) + C

2006-08-16 00:26:03 · answer #3 · answered by Anonymous · 1⤊ 0⤋