请问下这道高数题怎么做?不定积分

2025-01-24 05:33:13
推荐回答(1个)
回答1:

∫(1-x)/√(9-x^2)dx
=∫1/√(9-x^2)dx-∫x/√(9-x^2)dx
=∫1/√[1-(x/3)^2]d(x/3)+1/2∫1/√(9-x^2)d(9-x^2)
=arcsin(x/3)+1/2×1/(-1/2+1)(9-x^2)^(-1/2+1)+C
=arcsin(x/3)+(1/4)√(9-x^2)+C