(2x+3)/(根下1+2x-x^2)的不定积分
问题描述：
(2x+3)/(根下1+2x-x^2)的不定积分
答
∫(2x+3)/√(1+2x-x^2)dx=-∫(-2x+2)/(1+2x-x^2)dx+∫5/(1+2x-x^2)dx
=-∫d(1+2x-x^2)/√(1+2x-x^2)+5∫d[(x-1)/2√]/√1-[(x-1)/2√]^2
=-2√(1+2x-x^2)+5arctan(x-1)/√2+C