求∫dx/(a^2sin^2x+b^2cos^2x)解答

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/06/06 11:04:50

∫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

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