2.计算下列定积分:-|||-(1) (int )_(dfrac {pi )(3)}^pi sin (x+dfrac (pi )(3))dx;-|||-(2) (int )_(-2)^1dfrac (dx)({(11+5x))^3}-|||-(3) (int )_(0)^dfrac (pi {2)}sin varphi (cos )^3varphi (varphi )varphi varphi ;-|||-(4) (int )_(0)^pi (1-(sin )^3theta )dtheta ;-|||-(5) (int )_(dfrac {pi )(6)}^dfrac (pi {2)}(cos )^2udu;-|||-(6) (int )_(0)^sqrt (2)sqrt (2-{x)^2}dx;-|||-(7) (int )_(-sqrt {2)}^sqrt (2)sqrt (8-2{y)^2}dy;-|||-(8) (int )_(dfrac {1)(sqrt {2)}}dfrac (sqrt {1-{x)^2}}({x)^2}dx-|||-(9) (int )_(0)^a(x)^2sqrt ({a)^2-(x)^2}dx(agt 0);-|||-(10) (int )_(1)^sqrt (3)dfrac (dx)({x)^2sqrt (1+{x)^2}}-|||-(11) (int )_(-1)^1dfrac (xdx)(sqrt {5-4x)}-|||-(12) (int )_(1)^4dfrac (dx)(1+sqrt {x)}-|||-(13) (int )_(dfrac {3)(4)}^1dfrac (dx)(sqrt {1-x)-1};-|||-(14) (int )_(0)^sqrt (2a)dfrac (xdx)(sqrt {3{a)^2-(x)^2}}(agt 0)-|||-15) (int )_(0)^1t(e)^dfrac ({t^2)(2)dt};-|||-(16) (int )_(1)^(x^2)dfrac (dx)(xsqrt {1+ln x)}-|||-(17)[(x+2)/(202)dx/;(18)-|||-(int )_(0)^2dfrac (xdx)({({x)^2-2x+2)}^2}-|||-(19) (int )_(-pi )^pi (x)^4sin xdx;-|||-(20) (int )_(-dfrac {pi )(2)}^dfrac (pi {2)}4(cos )^4theta dtheta ;-|||-(21)1/2(arcsinx)^2 dx;-|||-(22) (int )_(-5)^5dfrac ({x)^3(sin )^2x}({x)^4+2(x)^2+1}dx-|||-(23) (int )_(-dfrac {pi )(2)}^dfrac (pi {2)}cos xcos 2xdx;-|||-(24)-|||-(int )_(-dfrac {pi )(2)}^dfrac (pi {2)}sqrt (cos x-{cos )^3x}dx-|||-(25) (int )_(0)^pi sqrt (1+cos 2x)dx;-|||-(26) (int )_(0)^2pi |sin (x+1)|dx;-|||-(27) (int )_(0)^dfrac (pi {4)}ln (1+tan x)dx;-|||-(28) (int )_(0)^adfrac (dx)(x+sqrt {{a)^2-(x)^2}}(agt 0);-|||-__-|||-(29) (int )_(0)^dfrac (pi {2)}sqrt (1-sin 2x)dx-|||-(30)(int )_(0)^dfrac (pi {2)}dfrac (dx)(1+{cos )^2x}-|||-(31) (int )_(0)^pi xsqrt ({cos )^2x-(cos )^4x}dx;-|||-(32) (int )_(0)^xmax {t)^3,(t)^2,1} dt;-|||-(33) (int )_(0)^1x((2-{x)^2)}^12dx;-|||-(34) (int )_(-1)^1dfrac (xdx)({x)^2+x+1}-|||-(35) (int )_(0)^dfrac (pi {2)}sin xsin 2xsin 3xdx-|||-36) (int )_(1)^2|1-x|dx;-|||-2 0≤x≤1,-|||-(37) (int )_(0)^2f(x)dx, 其中f(x)= 2-x,1