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

类似地，求极限lim_(ntoinfty)nint_(0)^1x^nsqrt(1+x^2)dx.类似地，求极限$\lim_{n\to\infty}n\int_{

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

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

求极限lim _(xarrow +infty )x(sqrt (1+{x)^2}-x)。求极限。

求极限lim _(xarrow +infty )x(sqrt (1+{x)^2}-x)。求极限。

例2 求 int dfrac (dx)(1+{x)^2} =

求极限 lim _(xarrow +infty )((x+sqrt {1+{x)^2})}^dfrac (1{x)}

求(int )_(-1)^1xln (1+(e)^x)dx.求.

求不定积分int (x)^2(ln x-dfrac (1)(1+{x)^2})dx.求不定积分.

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