求∫dx/(a^2sin^2x+b^2cos^2x)解答

来源:学生作业帮助网 编辑:六六作业网 时间:2024/05/25 14:21:07
求∫dx/(a^2sin^2x+b^2cos^2x)解答求∫dx/(a^2sin^2x+b^2cos^2x)解答求∫dx/(a^2sin^2x+b^2cos^2x)解答∫dx/(a^2sin^2x+b

求∫dx/(a^2sin^2x+b^2cos^2x)解答
求∫dx/(a^2sin^2x+b^2cos^2x)解答

求∫dx/(a^2sin^2x+b^2cos^2x)解答
∫dx/(a^2sin^2x+b^2cos^2x)
=∫dx/a^2*cos^2x*(tan^2x+b^2/a^2)
=1/a^2∫sec^2xdx/(tan^2x+b^2/a^2)
=1/a^2∫d(tanx)/(tan^2x+(b/a)^2)
=1/a^2*a/b*arctan(ax/b)+C
=(1/ab)*arctan(ax/b)+C