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

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

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

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

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

int dfrac (sin x)(1+{cos )^2x}dx=-|||-__

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

.int dfrac (1+{cos )^2x}(1+cos 2x)dx

[题目]求 int dfrac (arctan {e)^x}({e)^2x}dx

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

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