Question

Integral dx by cosec4x - cot4x

Answer 1

$\bf \: HELLO \: \: DEAR, \\ \\ \bf \int \frac{dx}{cosex4x - cot4x} \\ \\ \bf \int \frac{dx}{cosec4x - cot4x} * \frac{cosec4x + cot4x}{cosec4x + cot4x} \\ \\ \\ \bf \int \frac{dx(cosec4x + cot4x)}{(cosec^{2}4x - cot^{2}4x) } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \therefore \boxed{\bf cosec^{2}A - cot^{2}A = 1} \\ \\ \\ \bf \int cosec4x. dx + \int cot4x .dx \\ \\ \\ \bf \frac{1}{4} log|cosec4x - cot4x| + \frac{1}{4} log|sin4x| + c \\ \\ \\ \underline{\bf I \: \: HOPE \: \: ITS \: \: HELP \: \: YOU \: \: DEAR, \: \: THANKS}$