积分号2x+2/x^2+2x+5怎样换元法

Question

积分号2x+2/x^2+2x+5怎样换元法

Answer 1

∫[（2x+2）/(x^2+2x+5)]dx
=∫[1/(x^2+2x+5)]d(x^2+2x+5)
=ln(x^2+2x+5)
2x+2提到dx 里面,其实就是d(x^2+2x)至于加多少对于积分没影响,即d(x^2+2x+C) C为任意常数.