用不定积分第二换元法解道题 ∫ 1/(x+√1-x²)dx
问题描述：
用不定积分第二换元法解道题 ∫ 1/(x+√1-x²)dx
答
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...