Question

求解两道不定积分题

∫（cos2x/cos方x*sin方x）dx
∫（1/sin方xcos方x）dx
麻烦写一下详细步骤

Answer 1

1.
∫cos(2x)/(cos²xsin²x) dx
=∫cos(2x)sec²xcsc²x dx
=4∫cot(2x)csc(2x)dx
=2∫cot(2x)csc(2x)d(2x)
=2*-csc(2x)+C
=-2csc(2x)+C

2.
∫1/(sin²xcos²x) dx
=∫sec²xcsc²x dx
=4∫csc²(2x)dx
=2∫csc²(2x)d(2x)
=2*-cot(2x)+C
=-2cot(2x)+C