定积分∫x*tanx*secx^2dx范围是0到π/4

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定积分∫x*tanx*secx^2dx范围是0到π/4

定积分∫x*tanx*secx^2dx范围是0到π/4
定积分∫x*tanx*secx^2dx范围是0到π/4

定积分∫x*tanx*secx^2dx范围是0到π/4
详解见图、点击放大:

原式=∫xtanxdtanx
=1/2∫xdtan²x
=1/2xtan²x-1/2∫tan²xdx
=1/2xtan²x-1/2∫(sec²x-1)dx
=1/2xtan²x-1/2tanx+x/2(0到π/4)
=(π/8-1/2+π/8)-(0-0+0)
=π/4-1/2