Question

抛物线y=1/2 x^2+3x+5/2的对称轴是_______，在这条抛物线上有两个点M(x_1，

Answer 1

Answer 2

设(2x2-3x-3)/[(x-1)(x2-2x+5)]=[a/(x-1)]+[(bx+c)/(x2-2x+5)] 则2x2-3x-3=a(x2-2x+5)+(bx+c)(x-1) 整理得 2x2-3x-3=(a+b)x2-(2a+b-c)x+(5a-c) ∴a+b=2 2a+b-c=3 5a-c=-3 解得 a=-1 b=3 c=-2 ∴(2x2-3x-3)/[(x-1)(x2-2x+5)]=[-1/(x-1)]+[(3x-2)/(x2-2x+5)] ∴∫(2x2-3x-3)/[(x-1)(x2-2x+5)]dx =∫[-1/(x-1)]dx+∫[(3x-2)/(x2-2x+5)]dx =-ln|x-1|+∫[(3/2)(2x-2)/(x2-2x+5)]dx+∫[1/(x2-2x+5)]dx =-ln|x-1|+(3/2)ln|x2-2x+5|+∫[1/((x-1)2+4)]dx =-ln|x-1|+(3/2)ln|x2-2x+5|+(1/4)∫[1/(((x-1)/2)2+1)]dx =-ln|x-1|+(3/2)ln|x2-2x+5|+(1/2)∫[1/(((x-1)/2)2+1)]d[(x-1)/2] =-ln|x-1|+(3/2)ln|x2-2x+5|+(1/2)arctan[(x-1)/2]+C C为任意常数