1/(4x^2+4x+5)的不定积分怎么求的啊?

题目

1/(4x^2+4x+5)的不定积分怎么求的啊?

答案

∫dx/(4x^2+4x+5)=
=∫dx/[(2x+1)²+2²]=
=(1/4)∫dx/[(x+1/2)²+1]=
=(1/4)∫d(x+1/2)/[(x+1/2)²+1]=
=(1/4)arctan(x+1/2)+c