xarcsin(1/x)有原函数吗,

Question

xarcsin(1/x)有原函数吗,

Answer 1

有的,可用分部积分法来求：原函数=x²/2*arcsin(1/x)- ∫x²/2 1/√(1-1/x²)*(-1/x²)dx=x²/2*arcsin(1/x)+1/2∫x/√(x²-1)dx=x²/2*arcsin(1/x)+1/4∫d(x²-1)/√(x²-1)=1...