∫dx/(sinx+tanx)
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/08/19 01:04:31
∫dx/(sinx+tanx)
![∫dx/(sinx+tanx)](/uploads/image/z/19239665-41-5.jpg?t=%E2%88%ABdx%2F%28sinx%2Btanx%29)
三角函数万能公式
令tanx/2=t
(secx/2)^2dx/2=dt
dx=2dt/(t^2+1)
∫dx/(sinx+tanx)
=∫2dt/{(t^2+1)*[2t/(1+t^2)+2t/(1-t^2)]}
=∫dt/{(1+t^2)*2t/[(1+t^2)(1-t^2)]}
=∫(1-t^2)/(2t)dt
=1/2∫(1/t-t)dt
=1/2lnt-t^2/4+c
=1/2ln[tan(x/2)]-[tan(x/2)]^2/4+c
令tanx/2=t
(secx/2)^2dx/2=dt
dx=2dt/(t^2+1)
∫dx/(sinx+tanx)
=∫2dt/{(t^2+1)*[2t/(1+t^2)+2t/(1-t^2)]}
=∫dt/{(1+t^2)*2t/[(1+t^2)(1-t^2)]}
=∫(1-t^2)/(2t)dt
=1/2∫(1/t-t)dt
=1/2lnt-t^2/4+c
=1/2ln[tan(x/2)]-[tan(x/2)]^2/4+c
求不定积分 ∫ dx/(sinx+tanx)
求∫1/((tanx)^2+(sinx)^2)dx不定积分
求不定积分=∫sinx/(1+(tanx)^2)dx
求不定积分∫TANX/(3SINX^2+COSX^2)DX
∫dx/(1+tanx)
∫(tanx+x)dx
求定积分=∫sinx/(1+(tanx)^2)dx(-π/4
为什么 求不定积分∫sinx/cos^3x dx 答案不是1/2tanx^2
求∫tanx/(1-(tanx)^2)dx
微积分中tanx=(1-cosx)/sinx和tanx=sinx/(1+cosx)有什么区别?怎么用?例如∫dx/(1+
∫(tanx)^3(secx)dx
不定积分:∫ln|tanx|dx