2 / 4*acsc(2*x) 12 acsc(2*x) \
acsc (2*x)*|--------------- + ---------- + ------------------|
| __________ / 1 \ 3/2|
| / 1 x*|4 - --| 2 / 1 \ |
| / 1 - ---- | 2| 2*x *|1 - ----| |
| / 2 \ x / | 2| |
\\/ 4*x \ 4*x / /
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3
x
$$\frac{\left(\frac{4 \operatorname{acsc}{\left(2 x \right)}}{\sqrt{1 - \frac{1}{4 x^{2}}}} + \frac{12}{x \left(4 - \frac{1}{x^{2}}\right)} + \frac{\operatorname{acsc}{\left(2 x \right)}}{2 x^{2} \left(1 - \frac{1}{4 x^{2}}\right)^{\frac{3}{2}}}\right) \operatorname{acsc}^{2}{\left(2 x \right)}}{x^{3}}$$
/ 2 2 2 \
| 3 12*acsc (2*x) 36*acsc(2*x) 72*acsc(2*x) 3*acsc (2*x) 7*acsc (2*x) |
-|---------------- + --------------- + ------------ + ------------ + ------------------ + ------------------|*acsc(2*x)
| 3/2 __________ 2 / 1 \ 5/2 3/2|
| 2 / 1 \ / 1 3 / 1 \ x*|4 - --| 4 / 1 \ 2 / 1 \ |
|x *|1 - ----| / 1 - ---- x *|4 - --| | 2| 8*x *|1 - ----| 2*x *|1 - ----| |
| | 2| / 2 | 2| \ x / | 2| | 2| |
\ \ 4*x / \/ 4*x \ x / \ 4*x / \ 4*x / /
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4
x
$$- \frac{\left(\frac{12 \operatorname{acsc}^{2}{\left(2 x \right)}}{\sqrt{1 - \frac{1}{4 x^{2}}}} + \frac{72 \operatorname{acsc}{\left(2 x \right)}}{x \left(4 - \frac{1}{x^{2}}\right)} + \frac{7 \operatorname{acsc}^{2}{\left(2 x \right)}}{2 x^{2} \left(1 - \frac{1}{4 x^{2}}\right)^{\frac{3}{2}}} + \frac{3}{x^{2} \left(1 - \frac{1}{4 x^{2}}\right)^{\frac{3}{2}}} + \frac{36 \operatorname{acsc}{\left(2 x \right)}}{x^{3} \left(4 - \frac{1}{x^{2}}\right)^{2}} + \frac{3 \operatorname{acsc}^{2}{\left(2 x \right)}}{8 x^{4} \left(1 - \frac{1}{4 x^{2}}\right)^{\frac{5}{2}}}\right) \operatorname{acsc}{\left(2 x \right)}}{x^{4}}$$