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

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

( 单选题 ) int dfrac ({e)^x}(1+{e)^2x}dx=_________int dfrac ({e)^x}(1+{e)^2x}dx=int

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

(9) int dfrac (x{e)^arctan x}({(1+{x)^2)}^dfrac (3{2)}}dx ;

int dfrac ({x)^3}({(1+{x)^2)}^2}dx=A.int dfrac ({x)^3}({(1+{x)^2)}^2}dx=B.int df

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

(int )_(e)^+infty dfrac (dx)(x{ln )^2x}= __

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

int dfrac (dx)(sqrt {1+{e)^x}}

[例3]求极限 lim _(narrow infty )(int )_(0)^1(x)^nsqrt (1+{x)^2}dx.