43
cot (x) 31 43
32*8 *asin (x) cot (x) 32 42 / 2 \
---------------------- + 8 *asin (x)*cot (x)*\-43 - 43*cot (x)/*log(8)
________
/ 2
\/ 1 - x
$$8^{\cot^{43}{\left(x \right)}} \left(- 43 \cot^{2}{\left(x \right)} - 43\right) \log{\left(8 \right)} \cot^{42}{\left(x \right)} \operatorname{asin}^{32}{\left(x \right)} + \frac{32 \cdot 8^{\cot^{43}{\left(x \right)}} \operatorname{asin}^{31}{\left(x \right)}}{\sqrt{- x^{2} + 1}}$$
43 / 42 / 2 \ \
cot (x) 30 | 992 32*x*asin(x) 2752*cot (x)*\1 + cot (x)/*asin(x)*log(8) 2 41 / 2 \ / 2 43 / 2 \ \ |
8 *asin (x)*|- ------- + ------------ - ------------------------------------------ + 43*asin (x)*cot (x)*\1 + cot (x)/*\42 + 44*cot (x) + 43*cot (x)*\1 + cot (x)/*log(8)/*log(8)|
| 2 3/2 ________ |
| -1 + x / 2\ / 2 |
\ \1 - x / \/ 1 - x /
$$8^{\cot^{43}{\left(x \right)}} \left(43 \left(\cot^{2}{\left(x \right)} + 1\right) \left(43 \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(8 \right)} \cot^{43}{\left(x \right)} + 44 \cot^{2}{\left(x \right)} + 42\right) \log{\left(8 \right)} \cot^{41}{\left(x \right)} \operatorname{asin}^{2}{\left(x \right)} - \frac{2752 \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(8 \right)} \cot^{42}{\left(x \right)} \operatorname{asin}{\left(x \right)}}{\sqrt{- x^{2} + 1}} + \frac{32 x \operatorname{asin}{\left(x \right)}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} - \frac{992}{x^{2} - 1}\right) \operatorname{asin}^{30}{\left(x \right)}$$
43 / 2 2 2 / 2 2 2 \ 2 41 / 2 \ / 2 43 / 2 \ \ \
cot (x) 29 | 29760 32*asin (x) 96*x *asin (x) 2976*x*asin(x) 42 / 2 \ / 31 x*asin(x) \ 3 40 / 2 \ | 4 / 2 \ 2 / 2 \ 45 / 2 \ / 2 \ 86 2 / 2 \ 43 | 4128*asin (x)*cot (x)*\1 + cot (x)/*\42 + 44*cot (x) + 43*cot (x)*\1 + cot (x)/*log(8)/*log(8)|
8 *asin (x)*|----------- + ----------- + -------------- + -------------- - 4128*cot (x)*\1 + cot (x)/*|- ------- + -----------|*asin(x)*log(8) - 43*asin (x)*cot (x)*\1 + cot (x)/*\4*cot (x) + 1722*\1 + cot (x)/ + 254*cot (x)*\1 + cot (x)/ + 258*cot (x)*\1 + cot (x)/*log(8) + 1849*\1 + cot (x)/ *cot (x)*log (8) + 5418*\1 + cot (x)/ *cot (x)*log(8)/*log(8) + ------------------------------------------------------------------------------------------------|
| 3/2 3/2 5/2 2 | 2 3/2| ________ |
|/ 2\ / 2\ / 2\ / 2\ | -1 + x / 2\ | / 2 |
\\1 - x / \1 - x / \1 - x / \-1 + x / \ \1 - x / / \/ 1 - x /
$$8^{\cot^{43}{\left(x \right)}} \left(- 4128 \left(\frac{x \operatorname{asin}{\left(x \right)}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} - \frac{31}{x^{2} - 1}\right) \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(8 \right)} \cot^{42}{\left(x \right)} \operatorname{asin}{\left(x \right)} - 43 \left(\cot^{2}{\left(x \right)} + 1\right) \left(1849 \left(\cot^{2}{\left(x \right)} + 1\right)^{2} \log{\left(8 \right)}^{2} \cot^{86}{\left(x \right)} + 258 \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(8 \right)} \cot^{45}{\left(x \right)} + 5418 \left(\cot^{2}{\left(x \right)} + 1\right)^{2} \log{\left(8 \right)} \cot^{43}{\left(x \right)} + 4 \cot^{4}{\left(x \right)} + 254 \left(\cot^{2}{\left(x \right)} + 1\right) \cot^{2}{\left(x \right)} + 1722 \left(\cot^{2}{\left(x \right)} + 1\right)^{2}\right) \log{\left(8 \right)} \cot^{40}{\left(x \right)} \operatorname{asin}^{3}{\left(x \right)} + \frac{4128 \left(\cot^{2}{\left(x \right)} + 1\right) \left(43 \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(8 \right)} \cot^{43}{\left(x \right)} + 44 \cot^{2}{\left(x \right)} + 42\right) \log{\left(8 \right)} \cot^{41}{\left(x \right)} \operatorname{asin}^{2}{\left(x \right)}}{\sqrt{- x^{2} + 1}} + \frac{2976 x \operatorname{asin}{\left(x \right)}}{\left(x^{2} - 1\right)^{2}} + \frac{96 x^{2} \operatorname{asin}^{2}{\left(x \right)}}{\left(- x^{2} + 1\right)^{\frac{5}{2}}} + \frac{32 \operatorname{asin}^{2}{\left(x \right)}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} + \frac{29760}{\left(- x^{2} + 1\right)^{\frac{3}{2}}}\right) \operatorname{asin}^{29}{\left(x \right)}$$