Question 287733
<pre><font size = 4 color = "indigo"><b>
If you know these four formulas, which are in all
calculus books: 

{{{int("csc(u)cot(u)",du)=-csc(u)+C}}}
{{{int("sec(u)tan(u)",du)=sec(u)+C}}}
{{{d/(dx)}}}{{{sec(u)="[sec(u)tan(u)]u'"}}}
{{{d/(dx)}}}{{{csc(u)=-"[csc(u)cot(u)]u'"}}}

then your problem is immediate:

{{{int( "[csc(y)cot(y)"-"sec(y)tan(y)]", dy )}}}

{{{int("csc(y)cot(y)",dy)-int("sec(y)tan(y)",dy )}}}

{{{-csc(y)-sec(y)+C}}}

Checking, taking the derivative:

{{{-"[-csc(y)cot(y)]"-"sec(y)tan(y)"+0}}}

{{{"csc(y)cot(y)"-"sec(y)tan(y)"}}}

which is the function between the integral sign and the {{{dy}}}.

Edwin</pre>