令x=sinu,√(1-x²)=cosu,dx=cosudu∫1/(x+√(1-x²))dx=∫1/(sinu+cosu)*(cosu)du=∫cosu/(sinu+cosu)du=1/2∫(cosu+sinu+cosu-sinu)/(sinu+cosu)du=1/2∫(cosu+sinu)/(sinu+cosu)du+1/2∫(cosu-sinu)/(sin...