Question 1206383
<pre>
iii) Find the exact value of *integral* (with limit pi/4 and pi/6) cosec 2x dx, giving your answer in the form alnb.

Use the formula:

{{{int(cosec(u^""),du)}}}{{{""=""}}}{{{ln(tan^""(u/2)^""^"")+ C}}}




{{{int(cosec(2x),dx,pi/6,pi/4)}}}{{{""=""}}}{{{expr(1/2)int(cosec(2x),(2dx),pi/6,pi/4)}}}{{{""=""}}}{{{expr(1/2)ln(tan^""(2x/2)^""^"")}}}{{{matrix(3,2,

"|",pi/4,
"|","",
"|",pi/6)}}}{{{""=""}}}{{{expr(1/2)ln(tan^""(x)^""^"")}}}{{{matrix(3,2,

"|",pi/4,
"|","",
"|",pi/6)}}}{{{""=""}}}{{{expr(1/2)(ln(tan(pi/4)^"")-ln(tan(pi/6)^"")^"")}}}{{{""=""}}}{{{expr(1/2)(ln(1^"")-ln(sqrt(3)/3)^"")}}}{{{""=""}}}{{{expr(1/2)(0-ln(sqrt(3)/3)^"")}}}{{{""=""}}}

{{{expr(-1/2)ln(sqrt(3)/3)}}}{{{""=""}}}{{{-expr(1/2)(ln(sqrt(3))-ln(3^"")^"")}}}{{{""=""}}}{{{expr(-1/2)*(matrix(3,1,"",ln(3^(1/2)),"")-ln(3^""))}}}{{{""=""}}}{{{expr(-1/2)(expr(1/2)ln(3^"")-ln(3^"")^"")}}}{{{""=""}}}{{{expr(-1/2)(-expr(1/2)ln(3^"")^"")}}}{{{""=""}}}{{{expr(1/4)ln(3^"")}}}

Edwin</pre>