Question

不定积分∫dx/(x∧2√1-x∧2)

Answer 1

∫dx/(x²√1-x²) 分部法：u=1/√(1-x²),du=-xdx/√(1-x²),dv=dx/x²,v=-1/x,

=-1/[x√(1-x²)] - ∫(1/x)(xdx/√(1-x²)

=-1/[x√(1-x²)] - ∫dx/√(1-x²)

=-1/[x√(1-x²)] - arcsinx + C