Question

помогите решить интеграл
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Answer 1

$displaystyle intlimits {-frac{16}{sin x} } , dx = left|begin{array}{ccc}t = text{tg} dfrac{x}{2} \x = 2 , text{arctg} , t \ dx = dfrac{2}{1 + t^{2}}dt end{array}right| = intlimits {-dfrac{16}{sin (2 , text{arctg} , t)} } , dfrac{2}{1 + t^{2}}dt =$

$= -16displaystyle intlimits {dfrac{2(1 + t^{2})}{2t(1 + t^{2})} } , dt = -16int frac{dt}{t} = -16ln |t| + C = -16 ln left|text{tg} dfrac{x}{2} right| + C$