9、∫[-π/2,π/2][(1+x^3)cosx/(1+sin^2x)]dx=∫[-π/2,π/2][cosx/(1+sin^2x)]dx(被积函数是奇函数，定积分域关于原点对称的定积分值为0）=∫[-π/2,π/2]1/(1+sin^2x)dsinx=arctan(sinx)[-π/2,π/2]=arctan1-arctan(-1)=π/210、令atctanx=t.x=tant,dx=sec^2tdt,x=0,t=0,x=+∞，t=π/2原式=∫[0,π/2)tsec^2t/sec^3tdt=∫[0,π/2)tcostdt=tsint[0,π/2)-∫[0,π/2)sintdt=π/2-1...
|
