求arctanx^(1/2)/(x^1/2)*(1+x)的不定积分
问题描述:
求arctanx^(1/2)/(x^1/2)*(1+x)的不定积分
答
∫ arctan√x/[√x(1 + x)] dx
= ∫ 2arctan√x/[1 + (√x)²] d(√x)
= ∫ 2arctan√x d(arctan√x)
= (arctan√x)² + C