Question

Integral of cosec2x cot 2x 2x dx

Answer 1

$\large\bf \underline\red{Question:-}$

Integral of cosec2x cot 2x 2x dx

$\large\bf \underline\red{Answer:-}$

=> 1/2(Int [ sin 2x / (1 - cos 2x) + sin 2x/(1 + cos 2x) dx] ...

=> 1/2[ - ln|(1/(sin 2x) + (cos 2x) / (sin 2x)|] => 1/2[ - ln|(cosec 2x) + (cot 2x)|]

=> -1/2( ln | cosec 2x + cot 2x| + C. The required integral is -1/2(ln | cosec 2x + cot 2x| + C.