来源:学生作业帮 编辑:大师作文网作业帮 分类:综合作业 时间:2024/09/27 12:10:07
求不定积分问题,是用三角代换吗?求步骤
令x=sinu,dx=cosudu
∫dx/(x+√(1-x^2))
=∫cosudu/(sinu+cosu)
=1/2∫(cosu+sinu+cosu-sinu)du/(sinu+cosu)
=1/2∫[1+(cosu-sinu)/(sinu+cosu)]du
=1/2[u+ln|sinu+cosu|]+C
=1/2arcsinx+1/2ln|x+√(1-x^2)|+C