求微分dx/(4x^2+4x+5)
问题描述：
求微分dx/(4x^2+4x+5)
答
∫dx/(4x^2+4x+5)
=∫dx/(4x^2+4x+1+4)
=∫dx/[(2x+1)^2+4]
=∫dx/4{[(2x+1)/2]^2+1}
=1/4∫dx/{[(2x+1)/2]^2+1}
=1/4 *arctan[(2x+1)/2]+C