(2) (int )_(0)^dfrac (pi {2)}sin varphi (cos )^3varphi dvarphi ;

(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}

1.求下列不定积分:-|||-(12) int (cos )^2(omega t+varphi )sin (omega t+varphi )dt;

已知氢原子的 (varphi )_(2{p)_(2)}=dfrac (1)(4sqrt {2pi {{a)_(0)}^3}}(dfrac (r)({a)_(0)

(25) int (cos )^2(omega t+varphi )dt;

(25) int (cos )^2(omega t+varphi )dt;

设 M=int_(-(pi)/(2))^(pi)/(2) (sin x)/(1+x^2) cos^4 x dx，N=int_(-(pi)/(2))^(pi)/(

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

计算定积分：int_(0)^dfrac(pi {2)}(|sin x-cos x|{d)x}．计算定积分：$\int_{0}^{\dfrac{\pi }{2}}