2006-10-09 02:40:39 · 4 answers · asked by Sergio__ 7 in Science & Mathematics ➔ Mathematics
Int (x + 2)^(-2) dx = (x+2)^(-1)/(-1) + C = -1/(x+2) + C, C is a constant
2006-10-09 02:44:49 · answer #1 · answered by Steiner 7 · 3⤊ 0⤋
Integral of 1/(x+2)^2 = (x+2)^-1/-1 +c = -1/(x+2) +constant
2006-10-09 09:56:04 · answer #2 · answered by saki 2 · 0⤊ 0⤋
Use the substitution u=x+2. Then you're integrating 1/u^2 du.
Use the power rule: the antiderivative of u^n du is u^(n+1) / (n+1) + C, for n not equal to -1. In this case, n = -2, so you get
u^(-1) / (-1) + C = -1/u + C
Now write this in terms of x, by replacing u with x+2:
-1/(x+2) + C.
2006-10-09 09:48:51 · answer #3 · answered by James L 5 · 1⤊ 0⤋
let x+2=y
dx=dy
int(x+2)^-2 dx
=int y^-2dy
=-1/y
=-1/x+2
2006-10-09 09:50:35 · answer #4 · answered by openpsychy 6 · 1⤊ 0⤋