9/ x \ / 2 \ x 8/ x \
acos \3 + 2/*\15 + 15*tan (x)/ 9*3 *acos \3 + 2/*log(3)
- ------------------------------- - -----------------------------------
4 _______________
(5*tan(x) - 4) / 2
/ / x \ 3
\/ 1 - \3 + 2/ *(5*tan(x) - 4)
$$- \frac{\left(15 \tan^{2}{\left(x \right)} + 15\right) \operatorname{acos}^{9}{\left(3^{x} + 2 \right)}}{\left(5 \tan{\left(x \right)} - 4\right)^{4}} - \frac{9 \cdot 3^{x} \log{\left(3 \right)} \operatorname{acos}^{8}{\left(3^{x} + 2 \right)}}{\sqrt{- \left(3^{x} + 2\right)^{2} + 1} \left(5 \tan{\left(x \right)} - 4\right)^{3}}$$
/ / / 2 \ \ \
| 2/ x\ / 2 \ | 10*\1 + tan (x)/ | |
| / / x\ x x / x\ / x\\ 10*acos \2 + 3 /*\1 + tan (x)/*|- ---------------- + tan(x)| x / 2 \ / x\ |
7/ x\ | x 2 | acos\2 + 3 / 8*3 3 *\2 + 3 /*acos\2 + 3 /| \ -4 + 5*tan(x) / 90*3 *\1 + tan (x)/*acos\2 + 3 /*log(3)|
3*acos \2 + 3 /*|- 3*3 *log (3)*|------------------- + -------------- + ------------------------| - ------------------------------------------------------------ + ---------------------------------------|
| | _______________ 2 3/2 | -4 + 5*tan(x) _______________ |
| | / 2 / x\ / 2\ | / 2 |
| | / / x\ -1 + \2 + 3 / | / x\ | | / / x\ |
\ \\/ 1 - \2 + 3 / \1 - \2 + 3 / / / \/ 1 - \2 + 3 / *(-4 + 5*tan(x)) /
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
3
(-4 + 5*tan(x))
$$\frac{3 \left(- \frac{10 \left(\tan{\left(x \right)} - \frac{10 \left(\tan^{2}{\left(x \right)} + 1\right)}{5 \tan{\left(x \right)} - 4}\right) \left(\tan^{2}{\left(x \right)} + 1\right) \operatorname{acos}^{2}{\left(3^{x} + 2 \right)}}{5 \tan{\left(x \right)} - 4} - 3 \cdot 3^{x} \left(\frac{8 \cdot 3^{x}}{\left(3^{x} + 2\right)^{2} - 1} + \frac{3^{x} \left(3^{x} + 2\right) \operatorname{acos}{\left(3^{x} + 2 \right)}}{\left(- \left(3^{x} + 2\right)^{2} + 1\right)^{\frac{3}{2}}} + \frac{\operatorname{acos}{\left(3^{x} + 2 \right)}}{\sqrt{- \left(3^{x} + 2\right)^{2} + 1}}\right) \log{\left(3 \right)}^{2} + \frac{90 \cdot 3^{x} \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(3 \right)} \operatorname{acos}{\left(3^{x} + 2 \right)}}{\sqrt{- \left(3^{x} + 2\right)^{2} + 1} \cdot \left(5 \tan{\left(x \right)} - 4\right)}\right) \operatorname{acos}^{7}{\left(3^{x} + 2 \right)}}{\left(5 \tan{\left(x \right)} - 4\right)^{3}}$$
/ / / x\ x x / x\ / x\\ \
| / 2 \ x 2 / 2 \ | acos\2 + 3 / 8*3 3 *\2 + 3 /*acos\2 + 3 /| / x\ |
| | / 2 \ / 2 \ | 135*3 *log (3)*\1 + tan (x)/*|------------------- + -------------- + ------------------------|*acos\2 + 3 / |
| 3/ x\ / 2 \ | 2 250*\1 + tan (x)/ 60*\1 + tan (x)/*tan(x)| | _______________ 2 3/2 | / / 2 \ \ |
| / 2 \ 10*acos \2 + 3 /*\1 + tan (x)/*|1 + 3*tan (x) + ------------------ - -----------------------| | / 2 / x\ / 2\ | x 2/ x\ / 2 \ | 10*\1 + tan (x)/ | |
| | 2/ x\ 2*x 2*x 2/ x\ x / x\ 2*x / x\ / x\ x 2/ x\ / x\ 2*x / x\ 2/ x\| | 2 -4 + 5*tan(x) | | / / x\ -1 + \2 + 3 / | / x\ | | 270*3 *acos \2 + 3 /*\1 + tan (x)/*|- ---------------- + tan(x)|*log(3)|
6/ x\ | x 3 | acos \2 + 3 / 56*3 3 *acos \2 + 3 / 24*3 *acos\2 + 3 / 24*3 *\2 + 3 /*acos\2 + 3 / 3*3 *acos \2 + 3 /*\2 + 3 / 3*3 *\2 + 3 / *acos \2 + 3 /| \ (-4 + 5*tan(x)) / \\/ 1 - \2 + 3 / \1 - \2 + 3 / / / \ -4 + 5*tan(x) / |
3*acos \2 + 3 /*|- 3*3 *log (3)*|------------------- + ------------------ + ------------------ + ------------------ - ----------------------------- + --------------------------- + ------------------------------| - --------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------- + -----------------------------------------------------------------------|
| | _______________ 3/2 3/2 2 2 3/2 5/2 | -4 + 5*tan(x) -4 + 5*tan(x) _______________ |
| | / 2 / 2\ / 2\ / x\ / 2\ / 2\ / 2\ | / 2 |
| | / / x\ | / x\ | | / x\ | -1 + \2 + 3 / | / x\ | | / x\ | | / x\ | | / / x\ |
\ \\/ 1 - \2 + 3 / \1 - \2 + 3 / / \1 - \2 + 3 / / \-1 + \2 + 3 / / \1 - \2 + 3 / / \1 - \2 + 3 / / / \/ 1 - \2 + 3 / *(-4 + 5*tan(x)) /
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
3
(-4 + 5*tan(x))
$$\frac{3 \left(- \frac{10 \left(\tan^{2}{\left(x \right)} + 1\right) \left(3 \tan^{2}{\left(x \right)} - \frac{60 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{5 \tan{\left(x \right)} - 4} + 1 + \frac{250 \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\left(5 \tan{\left(x \right)} - 4\right)^{2}}\right) \operatorname{acos}^{3}{\left(3^{x} + 2 \right)}}{5 \tan{\left(x \right)} - 4} + \frac{135 \cdot 3^{x} \left(\tan^{2}{\left(x \right)} + 1\right) \left(\frac{8 \cdot 3^{x}}{\left(3^{x} + 2\right)^{2} - 1} + \frac{3^{x} \left(3^{x} + 2\right) \operatorname{acos}{\left(3^{x} + 2 \right)}}{\left(- \left(3^{x} + 2\right)^{2} + 1\right)^{\frac{3}{2}}} + \frac{\operatorname{acos}{\left(3^{x} + 2 \right)}}{\sqrt{- \left(3^{x} + 2\right)^{2} + 1}}\right) \log{\left(3 \right)}^{2} \operatorname{acos}{\left(3^{x} + 2 \right)}}{5 \tan{\left(x \right)} - 4} + \frac{270 \cdot 3^{x} \left(\tan{\left(x \right)} - \frac{10 \left(\tan^{2}{\left(x \right)} + 1\right)}{5 \tan{\left(x \right)} - 4}\right) \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(3 \right)} \operatorname{acos}^{2}{\left(3^{x} + 2 \right)}}{\sqrt{- \left(3^{x} + 2\right)^{2} + 1} \cdot \left(5 \tan{\left(x \right)} - 4\right)} - 3 \cdot 3^{x} \left(- \frac{24 \cdot 3^{2 x} \left(3^{x} + 2\right) \operatorname{acos}{\left(3^{x} + 2 \right)}}{\left(\left(3^{x} + 2\right)^{2} - 1\right)^{2}} + \frac{3^{2 x} \operatorname{acos}^{2}{\left(3^{x} + 2 \right)}}{\left(- \left(3^{x} + 2\right)^{2} + 1\right)^{\frac{3}{2}}} + \frac{3 \cdot 3^{2 x} \left(3^{x} + 2\right)^{2} \operatorname{acos}^{2}{\left(3^{x} + 2 \right)}}{\left(- \left(3^{x} + 2\right)^{2} + 1\right)^{\frac{5}{2}}} + \frac{24 \cdot 3^{x} \operatorname{acos}{\left(3^{x} + 2 \right)}}{\left(3^{x} + 2\right)^{2} - 1} + \frac{3 \cdot 3^{x} \left(3^{x} + 2\right) \operatorname{acos}^{2}{\left(3^{x} + 2 \right)}}{\left(- \left(3^{x} + 2\right)^{2} + 1\right)^{\frac{3}{2}}} + \frac{\operatorname{acos}^{2}{\left(3^{x} + 2 \right)}}{\sqrt{- \left(3^{x} + 2\right)^{2} + 1}} + \frac{56 \cdot 3^{2 x}}{\left(- \left(3^{x} + 2\right)^{2} + 1\right)^{\frac{3}{2}}}\right) \log{\left(3 \right)}^{3}\right) \operatorname{acos}^{6}{\left(3^{x} + 2 \right)}}{\left(5 \tan{\left(x \right)} - 4\right)^{3}}$$