求解，高等数学，不定积分，谢谢

Question

如题所述

Answer 1

1 + sint + cost
=(1+cost) + sint
=2cos²(t/2) + 2sin(t/2)*cos(t/2)
=2cos(t/2) * [cos(t/2) + sin(t/2)
=2cos²(t/2) * [1 + sin(t/2)/cos(t/2)]
=2cos²(t/2) * [1 + tan(t/2)]
则这个积分式可以变换为：
=∫dt * 1/2 * sec²(t/2)/[1 + tan(t/2)] 注：1/cos²θ = sec²θ
=∫d(t/2) * sec²(t/2) /[1+tan(t/2)] 注：1/2 * dt = d(t/2)
=∫d[tan(t/2)] /[1+tan(t/2)] 注：sec²θ*dθ = d(tanθ)
=∫d[tan(t/2) + 1]/[1 + tan(t/2)]
=ln[1+tan(t/2)] + C
=ln[sin(t/2)+cos(t/2)]/cos(t/2) + C
=ln[2sin²(t/2) + 2sin(t/2) * cos(t/2)]/[2sin(t/2) * cos(t/2)] + C
=ln[sint + 1 - cost]/(sint) + C
=ln(1 + cscx - ctgx) + C追问

谢谢你啦～～

ctg是什么函数？

Answer 2

追答