/ /7\ \
| tan|-| | / /7\ \
| \x/ / 2/7\\ | | tan|-| |
| 7*8 *|1 + tan |-||*log(8)| ___ 2/ _________\ | \x/ 8 |
3/ _________\ | 7 / 2 \ \ \x// | 3*\/ 5 *acos \\/ 5*x + 1 /*\8 + tan (7*x)/
acos \\/ 5*x + 1 /*|tan (7*x)*\56 + 56*tan (7*x)/ - ------------------------------| - ------------------------------------------------
| 2 | ____ _________
\ x / 2*\/ -x *\/ 5*x + 1
$$\left(\left(56 \tan^{2}{\left(7 x \right)} + 56\right) \tan^{7}{\left(7 x \right)} - \frac{7 \cdot 8^{\tan{\left(\frac{7}{x} \right)}} \left(\tan^{2}{\left(\frac{7}{x} \right)} + 1\right) \log{\left(8 \right)}}{x^{2}}\right) \operatorname{acos}^{3}{\left(\sqrt{5 x + 1} \right)} - \frac{3 \sqrt{5} \cdot \left(\tan^{8}{\left(7 x \right)} + 8^{\tan{\left(\frac{7}{x} \right)}}\right) \operatorname{acos}^{2}{\left(\sqrt{5 x + 1} \right)}}{2 \sqrt{- x} \sqrt{5 x + 1}}$$
/ / /7\ \ \
| | tan|-| | |
| / /7\ \ | \x/ / 2/7\\ | |
| / /7\ /7\ /7\ \ | tan|-| | / ___ / _________\ ___ / _________\\ | 8 *|1 + tan |-||*log(8)| |
| | tan|-| tan|-| 2 tan|-| | | \x/ 8 | | 10 5*\/ 5 *acos\\/ 1 + 5*x / \/ 5 *acos\\/ 1 + 5*x /| ___ | 7 / 2 \ \ \x// | / _________\|
| | \x/ / 2/7\\ \x/ / 2/7\\ 2 \x/ / 2/7\\ /7\| 3*\8 + tan (7*x)/*|- ----------- + ------------------------- + -----------------------| 21*\/ 5 *|- 8*tan (7*x)*\1 + tan (7*x)/ + ----------------------------|*acos\\/ 1 + 5*x /|
| | 2 2*8 *|1 + tan |-||*log(8) 7*8 *|1 + tan |-|| *log (8) 14*8 *|1 + tan |-||*log(8)*tan|-|| | x*(1 + 5*x) ____ 3/2 ____ _________ | | 2 | |
| 2/ _________\ | 8 / 2 \ / 2 \ 6 \ \x// \ \x// \ \x// \x/| \ \/ -x *(1 + 5*x) x*\/ -x *\/ 1 + 5*x / \ x / | / _________\
|7*acos \\/ 1 + 5*x /*|112*tan (7*x)*\1 + tan (7*x)/ + 392*\1 + tan (7*x)/ *tan (7*x) + ------------------------------ + -------------------------------- + --------------------------------------| + --------------------------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------|*acos\\/ 1 + 5*x /
| | 3 4 4 | 4 ____ _________ |
\ \ x x x / \/ -x *\/ 1 + 5*x /
$$\left(7 \cdot \left(112 \left(\tan^{2}{\left(7 x \right)} + 1\right) \tan^{8}{\left(7 x \right)} + 392 \left(\tan^{2}{\left(7 x \right)} + 1\right)^{2} \tan^{6}{\left(7 x \right)} + \frac{2 \cdot 8^{\tan{\left(\frac{7}{x} \right)}} \left(\tan^{2}{\left(\frac{7}{x} \right)} + 1\right) \log{\left(8 \right)}}{x^{3}} + \frac{7 \cdot 8^{\tan{\left(\frac{7}{x} \right)}} \left(\tan^{2}{\left(\frac{7}{x} \right)} + 1\right)^{2} \log{\left(8 \right)}^{2}}{x^{4}} + \frac{14 \cdot 8^{\tan{\left(\frac{7}{x} \right)}} \left(\tan^{2}{\left(\frac{7}{x} \right)} + 1\right) \log{\left(8 \right)} \tan{\left(\frac{7}{x} \right)}}{x^{4}}\right) \operatorname{acos}^{2}{\left(\sqrt{5 x + 1} \right)} + \frac{3 \cdot \left(\tan^{8}{\left(7 x \right)} + 8^{\tan{\left(\frac{7}{x} \right)}}\right) \left(- \frac{10}{x \left(5 x + 1\right)} + \frac{\sqrt{5} \operatorname{acos}{\left(\sqrt{5 x + 1} \right)}}{x \sqrt{- x} \sqrt{5 x + 1}} + \frac{5 \sqrt{5} \operatorname{acos}{\left(\sqrt{5 x + 1} \right)}}{\sqrt{- x} \left(5 x + 1\right)^{\frac{3}{2}}}\right)}{4} + \frac{21 \sqrt{5} \cdot \left(- 8 \left(\tan^{2}{\left(7 x \right)} + 1\right) \tan^{7}{\left(7 x \right)} + \frac{8^{\tan{\left(\frac{7}{x} \right)}} \left(\tan^{2}{\left(\frac{7}{x} \right)} + 1\right) \log{\left(8 \right)}}{x^{2}}\right) \operatorname{acos}{\left(\sqrt{5 x + 1} \right)}}{\sqrt{- x} \sqrt{5 x + 1}}\right) \operatorname{acos}{\left(\sqrt{5 x + 1} \right)}$$
/ / /7\ \ / /7\ /7\ /7\ \\
| | tan|-| | | tan|-| tan|-| 2 tan|-| ||
| / /7\ \ | \x/ / 2/7\\ | | \x/ / 2/7\\ \x/ / 2/7\\ 2 \x/ / 2/7\\ /7\||
| / /7\ /7\ /7\ /7\ /7\ /7\ /7\ \ | tan|-| | / / _________\ / _________\ ___ ___ 2/ _________\ ___ 2/ _________\ ___ 2/ _________\\ | 8 *|1 + tan |-||*log(8)| / ___ / _________\ ___ / _________\\ | 2 2*8 *|1 + tan |-||*log(8) 7*8 *|1 + tan |-|| *log (8) 14*8 *|1 + tan |-||*log(8)*tan|-|||
| | tan|-| tan|-| 2 tan|-| 3 tan|-| 2 tan|-| tan|-| tan|-| 2 | | \x/ 8 | | 150*acos\\/ 1 + 5*x / 30*acos\\/ 1 + 5*x / 10*\/ 5 75*\/ 5 *acos \\/ 1 + 5*x / 3*\/ 5 *acos \\/ 1 + 5*x / 10*\/ 5 *acos \\/ 1 + 5*x /| | 7 / 2 \ \ \x// | | 10 5*\/ 5 *acos\\/ 1 + 5*x / \/ 5 *acos\\/ 1 + 5*x /| / _________\ ___ 2/ _________\ | 8 / 2 \ / 2 \ 6 \ \x// \ \x// \ \x// \x/||
| | \x/ / 2/7\\ \x/ / 2/7\\ 2 \x/ / 2/7\\ 3 \x/ / 2/7\\ \x/ / 2/7\\ /7\ \x/ 2/7\ / 2/7\\ \x/ / 2/7\\ 2 /7\| 3*\8 + tan (7*x)/*|- --------------------- - -------------------- - --------------------- + --------------------------- + -------------------------- + ---------------------------| 63*|- 8*tan (7*x)*\1 + tan (7*x)/ + ----------------------------|*|- ----------- + ------------------------- + -----------------------|*acos\\/ 1 + 5*x / 63*\/ 5 *acos \\/ 1 + 5*x /*|112*tan (7*x)*\1 + tan (7*x)/ + 392*\1 + tan (7*x)/ *tan (7*x) + ------------------------------ + -------------------------------- + --------------------------------------||
| | 2 3 6*8 *|1 + tan |-||*log(8) 42*8 *|1 + tan |-|| *log (8) 49*8 *|1 + tan |-|| *log (8) 98*8 *|1 + tan |-|| *log(8) 84*8 *|1 + tan |-||*log(8)*tan|-| 196*8 *tan |-|*|1 + tan |-||*log(8) 294*8 *|1 + tan |-|| *log (8)*tan|-|| | 2 2 ____ 3/2 ____ 5/2 2 ____ _________ ____ 3/2 | | 2 | | x*(1 + 5*x) ____ 3/2 ____ _________ | | 3 4 4 ||
| 3/ _________\ | / 2 \ 7 / 2 \ 5 9 / 2 \ \ \x// \ \x// \ \x// \ \x// \ \x// \x/ \x/ \ \x// \ \x// \x/| \ x*(1 + 5*x) x *(1 + 5*x) x*\/ -x *(1 + 5*x) \/ -x *(1 + 5*x) x *\/ -x *\/ 1 + 5*x x*\/ -x *(1 + 5*x) / \ x / \ \/ -x *(1 + 5*x) x*\/ -x *\/ 1 + 5*x / \ x x x /|
-|7*acos \\/ 1 + 5*x /*|- 17248*\1 + tan (7*x)/ *tan (7*x) - 16464*\1 + tan (7*x)/ *tan (7*x) - 1568*tan (7*x)*\1 + tan (7*x)/ + ------------------------------ + --------------------------------- + --------------------------------- + -------------------------------- + -------------------------------------- + ---------------------------------------- + -----------------------------------------| + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| | 4 5 6 6 5 6 6 | 8 4 ____ _________ |
\ \ x x x x x x x / 2*\/ -x *\/ 1 + 5*x /
$$- (7 \cdot \left(- 1568 \left(\tan^{2}{\left(7 x \right)} + 1\right) \tan^{9}{\left(7 x \right)} - 17248 \left(\tan^{2}{\left(7 x \right)} + 1\right)^{2} \tan^{7}{\left(7 x \right)} - 16464 \left(\tan^{2}{\left(7 x \right)} + 1\right)^{3} \tan^{5}{\left(7 x \right)} + \frac{6 \cdot 8^{\tan{\left(\frac{7}{x} \right)}} \left(\tan^{2}{\left(\frac{7}{x} \right)} + 1\right) \log{\left(8 \right)}}{x^{4}} + \frac{42 \cdot 8^{\tan{\left(\frac{7}{x} \right)}} \left(\tan^{2}{\left(\frac{7}{x} \right)} + 1\right)^{2} \log{\left(8 \right)}^{2}}{x^{5}} + \frac{84 \cdot 8^{\tan{\left(\frac{7}{x} \right)}} \left(\tan^{2}{\left(\frac{7}{x} \right)} + 1\right) \log{\left(8 \right)} \tan{\left(\frac{7}{x} \right)}}{x^{5}} + \frac{49 \cdot 8^{\tan{\left(\frac{7}{x} \right)}} \left(\tan^{2}{\left(\frac{7}{x} \right)} + 1\right)^{3} \log{\left(8 \right)}^{3}}{x^{6}} + \frac{294 \cdot 8^{\tan{\left(\frac{7}{x} \right)}} \left(\tan^{2}{\left(\frac{7}{x} \right)} + 1\right)^{2} \log{\left(8 \right)}^{2} \tan{\left(\frac{7}{x} \right)}}{x^{6}} + \frac{196 \cdot 8^{\tan{\left(\frac{7}{x} \right)}} \left(\tan^{2}{\left(\frac{7}{x} \right)} + 1\right) \log{\left(8 \right)} \tan^{2}{\left(\frac{7}{x} \right)}}{x^{6}} + \frac{98 \cdot 8^{\tan{\left(\frac{7}{x} \right)}} \left(\tan^{2}{\left(\frac{7}{x} \right)} + 1\right)^{2} \log{\left(8 \right)}}{x^{6}}\right) \operatorname{acos}^{3}{\left(\sqrt{5 x + 1} \right)} + \frac{63 \cdot \left(- 8 \left(\tan^{2}{\left(7 x \right)} + 1\right) \tan^{7}{\left(7 x \right)} + \frac{8^{\tan{\left(\frac{7}{x} \right)}} \left(\tan^{2}{\left(\frac{7}{x} \right)} + 1\right) \log{\left(8 \right)}}{x^{2}}\right) \left(- \frac{10}{x \left(5 x + 1\right)} + \frac{\sqrt{5} \operatorname{acos}{\left(\sqrt{5 x + 1} \right)}}{x \sqrt{- x} \sqrt{5 x + 1}} + \frac{5 \sqrt{5} \operatorname{acos}{\left(\sqrt{5 x + 1} \right)}}{\sqrt{- x} \left(5 x + 1\right)^{\frac{3}{2}}}\right) \operatorname{acos}{\left(\sqrt{5 x + 1} \right)}}{4} + \frac{3 \cdot \left(\tan^{8}{\left(7 x \right)} + 8^{\tan{\left(\frac{7}{x} \right)}}\right) \left(- \frac{150 \operatorname{acos}{\left(\sqrt{5 x + 1} \right)}}{x \left(5 x + 1\right)^{2}} - \frac{30 \operatorname{acos}{\left(\sqrt{5 x + 1} \right)}}{x^{2} \cdot \left(5 x + 1\right)} + \frac{3 \sqrt{5} \operatorname{acos}^{2}{\left(\sqrt{5 x + 1} \right)}}{x^{2} \sqrt{- x} \sqrt{5 x + 1}} + \frac{10 \sqrt{5} \operatorname{acos}^{2}{\left(\sqrt{5 x + 1} \right)}}{x \sqrt{- x} \left(5 x + 1\right)^{\frac{3}{2}}} + \frac{75 \sqrt{5} \operatorname{acos}^{2}{\left(\sqrt{5 x + 1} \right)}}{\sqrt{- x} \left(5 x + 1\right)^{\frac{5}{2}}} - \frac{10 \sqrt{5}}{x \sqrt{- x} \left(5 x + 1\right)^{\frac{3}{2}}}\right)}{8} + \frac{63 \sqrt{5} \cdot \left(112 \left(\tan^{2}{\left(7 x \right)} + 1\right) \tan^{8}{\left(7 x \right)} + 392 \left(\tan^{2}{\left(7 x \right)} + 1\right)^{2} \tan^{6}{\left(7 x \right)} + \frac{2 \cdot 8^{\tan{\left(\frac{7}{x} \right)}} \left(\tan^{2}{\left(\frac{7}{x} \right)} + 1\right) \log{\left(8 \right)}}{x^{3}} + \frac{7 \cdot 8^{\tan{\left(\frac{7}{x} \right)}} \left(\tan^{2}{\left(\frac{7}{x} \right)} + 1\right)^{2} \log{\left(8 \right)}^{2}}{x^{4}} + \frac{14 \cdot 8^{\tan{\left(\frac{7}{x} \right)}} \left(\tan^{2}{\left(\frac{7}{x} \right)} + 1\right) \log{\left(8 \right)} \tan{\left(\frac{7}{x} \right)}}{x^{4}}\right) \operatorname{acos}^{2}{\left(\sqrt{5 x + 1} \right)}}{2 \sqrt{- x} \sqrt{5 x + 1}})$$