求∫cscxdx,下面是我的运算过程∫cscxdx=∫(1/sinx)dx=∫(sinx/sin^2x)dx=∫[1/(1-cos^2x)]*[-d(cosx)]=-∫[1/(1+cosx)(1-cosx)]dcosx=-1/2∫[(1+cosx+1-cosx)/(1+cosx)(1-cosx)]dcosx=-1/2∫[1/(1-cosx)+1/(1+cosx)]dcosx=-1/2∫{[1/(1-cosx)]d(1

Question

求∫csc xdx,下面是我的运算过程
∫csc xdx
=∫(1/sinx)dx
=∫(sinx/sin^2x)dx
=∫[1/(1-cos^2x)]*[-d(cosx)]
=-∫[1/(1+cosx)(1-cosx)]dcosx
=-1/2∫[(1+cosx+1-cosx)/(1+cosx)(1-cosx)]dcosx
=-1/2∫[1/(1-cosx)+1/(1+cosx)]dcosx
=-1/2∫{[1/(1-cosx)]d(1-cosx)+[1/(1+cosx)]d(1+cosx)}
=-1/2∫(ln l 1-cosx l+ln l 1+cosx l)
=-1/2ln(1-cos^2x)
=-1/2ln sin^2x+c
我这么算对吗

Answer 1

=-1/2∫(ln l 1-cosx l+ln l 1+cosx l)
到此即可