求不定积分(1/sin^2xcos^2x)dx

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求不定积分(1/sin^2xcos^2x)dx求不定积分(1/sin^2xcos^2x)dx求不定积分(1/sin^2xcos^2x)dx原式=∫4dx/(2sinxcosx)²=4∫dx/

求不定积分(1/sin^2xcos^2x)dx
求不定积分(1/sin^2xcos^2x)dx

求不定积分(1/sin^2xcos^2x)dx
原式=∫4dx/(2sinxcosx)²
=4∫dx/sin²2x
=2∫csc²2xd2x
=-2cot2x+C

原式=∫4/4sin^2xcos^2xdx
=∫4/sin^2(2x)dx
=2∫csc^2(2x)d(2x)
=-2ctg(2x)+C

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