4.下列结论正确的是 ()-|||-(A) (int )_(-infty )^+infty dfrac (x)(1+{x)^2}dx=0 (B) (int )_(-infty )^edfrac (1)(x)dx=0-|||-(C) (int )_(-dfrac {pi )(2)}^dfrac (pi {2)}((e)^x-(e)^-x)sin xdx=0 (D) (int )_(-1)^1sqrt [3](x(x+1)(x-1))dx=0

(4) (int )_(0)^+infty dfrac (dx)((1+x)(1+{x)^2)}

()-|||-(2) (int )_(-infty )^+infty dfrac (2x)(1+{x)^2}dx=lim _(aarrow +infty )(i

(int )_(0)^+infty dfrac (x{e)^-x}({(1+{e)^-x)}^2}dx= ()-|||-__

(int )_(-infty )^+infty (x)^2(e)^-a(x^2)dx=dfrac (1)(2)sqrt (dfrac {pi )({a)^3}}

10.若 (int )_(-infty )^+infty dfrac (A)(1+{x)^2}dx=1 则常数A等于:-|||-

计算(int )_(0)^+infty dfrac (dx)({x)^2+4x+3}的值是A (int )_(0)^+infty dfrac (dx)({x)^

[例3] (int )_(0)^+infty dfrac (x{e)^-x}({(1+{e)^-x)}^2}dx

B: (Xgt X)=(int )_(-infty )^xf(x)dx-|||-C: (int )_(-infty )^+infty f(x)dx=1 D: (

(int )_(-infty )^+infty dfrac (dx)({x)^2+2x+2}..

(2) (int )_(-infty )^+infty dfrac (dx)({x)^2+2x+2}