(int )_(-dfrac {pi )(2)}^dfrac (pi {2)}((cos )^2x+dfrac (xcos x)(1+{cos )^2x})dx=.

(int )_(0)^dfrac (pi {4)}dfrac (x)(1+cos 2x)dx=( ) .(int )_(0)^dfrac (pi {4)}dfr

(int )_(-dfrac {pi )(2)}^dfrac (pi {2)}dfrac (|x|sin x)(1+{cos )^3x}dx=(int )_(-

设=(int )_(-dfrac {pi )(2)}^dfrac (pi {2)}dfrac (sin x)(1+{x)^2}(cos )^4xdx, =(in

(sin x)=dfrac (1)({cos )^2x} in (0,dfrac (pi )(2)),则(sin x)=dfrac (1)({cos )^2x}

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

(3) (int )_(0)^dfrac (pi {4)}dfrac (x)(1+cos 2x)dx= () .-|||-(A) dfrac (pi )(8)+

lim _(xarrow dfrac {pi )(2)}dfrac (cos x)(pi -2x)..

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

例: (int )_(0)^dfrac (pi {2)}(cos )^2dfrac (x)(2)dx= __ .

【题目】-|||-dfrac (d)(dx)(int )_(sin x)^cos xcos (pi (t)^2)dt .