Question

高等数学积分

高等数学积分这题的步骤是什么？

Answer 1

有理函数积分，我用软件求解的。你可以参考一下，不懂可以问，望采纳！

Answer 2

就是这样！

Answer 3

半角代换，令 u = tan(x/2)， 则 x = 2arctanu， dx = 2du/(1+u^2),
I = ∫<-tan(π/8), tan(π/8)>[2du/(1+u^2)]/[1+2u/(1+u^2)]
= ∫<-tan(π/8), tan(π/8)>2du/(1+u)^2
= 2∫<-tan(π/8), tan(π/8)>d(1+u)/(1+u)^2
= 2[-1/(1+u)]<-tan(π/8), tan(π/8)>
= 2{1/[1-tan(π/8) - 1/[1+tan(π/8)]}
tan(π/8) = [1-cos(π/4)]/sin(π/4) = (1-1/√2)/(1/√2) = √2-1,
则 I = 2[1/(2-√2) - 1/√2] = 2

Answer 4

=∫(1-sinx)/cos²xdx
=∫sec²x-tanxsecxdx
=tanx-secx
=(1-√2)-(-1-√2)
=2