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

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

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

(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}}

4.下列结论正确的是 ()-|||-(A) (int )_(-infty )^+infty dfrac (x)(1+{x)^2}dx=0 (B) (int )_

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

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

求(int )_(1)^+infty dfrac (dx)(xsqrt {2{x)^2-1}}=求

[题目]计算 (int )_(1)^+infty dfrac (arctan x)({x)^2}dx

1.讨论下列无穷积分是否收敛?若收敛,则求其值:-|||-(1) (int )_(0)^+infty x(e)^-(x^2)dx;-|||-(2) (int )