8/3 3 5/3 4 8/3 4
12*(2*x + 3) *(3*x - 7) 16*(2*x + 3) *(3*x - 7) 3*(2*x + 3) *(3*x - 7)
-------------------------- + -------------------------- - -------------------------
3/x\ 3/x\ / 2\
atan |-| 3*atan |-| | x | 4/x\
\2/ \2/ 2*|1 + --|*atan |-|
\ 4 / \2/
$$\frac{12 \left(2 x + 3\right)^{\frac{8}{3}} \left(3 x - 7\right)^{3}}{\operatorname{atan}^{3}{\left(\frac{x}{2} \right)}} - \frac{3 \left(2 x + 3\right)^{\frac{8}{3}} \left(3 x - 7\right)^{4}}{2 \left(\frac{x^{2}}{4} + 1\right) \operatorname{atan}^{4}{\left(\frac{x}{2} \right)}} + \frac{16 \left(2 x + 3\right)^{\frac{5}{3}} \left(3 x - 7\right)^{4}}{3 \operatorname{atan}^{3}{\left(\frac{x}{2} \right)}}$$
/ 2 2 / 4 \\
| 3*(-7 + 3*x) *(3 + 2*x) *|x + -------||
| | /x\||
| 2 2 2 | atan|-|||
2 2/3 | 2 40*(-7 + 3*x) 36*(3 + 2*x) *(-7 + 3*x) 16*(-7 + 3*x) *(3 + 2*x) \ \2//|
4*(-7 + 3*x) *(3 + 2*x) *|27*(3 + 2*x) + -------------- + 32*(-7 + 3*x)*(3 + 2*x) - ------------------------ - ------------------------ + --------------------------------------|
| 9 / 2\ /x\ / 2\ /x\ 2 |
| \4 + x /*atan|-| \4 + x /*atan|-| / 2\ /x\ |
| \2/ \2/ \4 + x / *atan|-| |
\ \2/ /
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
3/x\
atan |-|
\2/
$$\frac{4 \left(2 x + 3\right)^{\frac{2}{3}} \left(3 x - 7\right)^{2} \cdot \left(\frac{3 \left(x + \frac{4}{\operatorname{atan}{\left(\frac{x}{2} \right)}}\right) \left(2 x + 3\right)^{2} \left(3 x - 7\right)^{2}}{\left(x^{2} + 4\right)^{2} \operatorname{atan}{\left(\frac{x}{2} \right)}} + 27 \left(2 x + 3\right)^{2} + 32 \cdot \left(2 x + 3\right) \left(3 x - 7\right) + \frac{40 \left(3 x - 7\right)^{2}}{9} - \frac{36 \left(2 x + 3\right)^{2} \cdot \left(3 x - 7\right)}{\left(x^{2} + 4\right) \operatorname{atan}{\left(\frac{x}{2} \right)}} - \frac{16 \cdot \left(2 x + 3\right) \left(3 x - 7\right)^{2}}{\left(x^{2} + 4\right) \operatorname{atan}{\left(\frac{x}{2} \right)}}\right)}{\operatorname{atan}^{3}{\left(\frac{x}{2} \right)}}$$
/ / 2 \ \
| 3 8/3 | 4*x 40 24*x | 3 5/3 / 4 \ 2 8/3 / 4 \|
| 3*(-7 + 3*x) *(3 + 2*x) *|-1 + ------ + ----------------- + ----------------| 48*(-7 + 3*x) *(3 + 2*x) *|x + -------| 108*(-7 + 3*x) *(3 + 2*x) *|x + -------||
| | 2 / 2\ 2/x\ / 2\ /x\| | /x\| | /x\||
| 3 2 5/3 8/3 3 2/3 | 4 + x \4 + x /*atan |-| \4 + x /*atan|-|| | atan|-|| | atan|-|||
| 8/3 2 2/3 5/3 160*(-7 + 3*x) 576*(-7 + 3*x) *(3 + 2*x) 486*(3 + 2*x) *(-7 + 3*x) 80*(-7 + 3*x) *(3 + 2*x) \ \2/ \2// \ \2// \ \2//|
4*(-7 + 3*x)*|162*(3 + 2*x) + 160*(-7 + 3*x) *(3 + 2*x) + 432*(3 + 2*x) *(-7 + 3*x) + --------------- - ---------------------------- - --------------------------- - --------------------------- - ------------------------------------------------------------------------------- + ----------------------------------------- + ------------------------------------------|
| 3 _________ / 2\ /x\ / 2\ /x\ / 2\ /x\ 2 2 2 |
| 27*\/ 3 + 2*x \4 + x /*atan|-| \4 + x /*atan|-| \4 + x /*atan|-| / 2\ /x\ / 2\ /x\ / 2\ /x\ |
| \2/ \2/ \2/ \4 + x / *atan|-| \4 + x / *atan|-| \4 + x / *atan|-| |
\ \2/ \2/ \2/ /
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
3/x\
atan |-|
\2/
$$\frac{4 \cdot \left(3 x - 7\right) \left(- \frac{3 \left(2 x + 3\right)^{\frac{8}{3}} \left(3 x - 7\right)^{3} \cdot \left(\frac{4 x^{2}}{x^{2} + 4} - 1 + \frac{24 x}{\left(x^{2} + 4\right) \operatorname{atan}{\left(\frac{x}{2} \right)}} + \frac{40}{\left(x^{2} + 4\right) \operatorname{atan}^{2}{\left(\frac{x}{2} \right)}}\right)}{\left(x^{2} + 4\right)^{2} \operatorname{atan}{\left(\frac{x}{2} \right)}} + \frac{108 \left(x + \frac{4}{\operatorname{atan}{\left(\frac{x}{2} \right)}}\right) \left(2 x + 3\right)^{\frac{8}{3}} \left(3 x - 7\right)^{2}}{\left(x^{2} + 4\right)^{2} \operatorname{atan}{\left(\frac{x}{2} \right)}} + 162 \left(2 x + 3\right)^{\frac{8}{3}} - \frac{486 \left(2 x + 3\right)^{\frac{8}{3}} \cdot \left(3 x - 7\right)}{\left(x^{2} + 4\right) \operatorname{atan}{\left(\frac{x}{2} \right)}} + \frac{48 \left(x + \frac{4}{\operatorname{atan}{\left(\frac{x}{2} \right)}}\right) \left(2 x + 3\right)^{\frac{5}{3}} \left(3 x - 7\right)^{3}}{\left(x^{2} + 4\right)^{2} \operatorname{atan}{\left(\frac{x}{2} \right)}} + 432 \left(2 x + 3\right)^{\frac{5}{3}} \cdot \left(3 x - 7\right) - \frac{576 \left(2 x + 3\right)^{\frac{5}{3}} \left(3 x - 7\right)^{2}}{\left(x^{2} + 4\right) \operatorname{atan}{\left(\frac{x}{2} \right)}} + 160 \left(2 x + 3\right)^{\frac{2}{3}} \left(3 x - 7\right)^{2} - \frac{80 \left(2 x + 3\right)^{\frac{2}{3}} \left(3 x - 7\right)^{3}}{\left(x^{2} + 4\right) \operatorname{atan}{\left(\frac{x}{2} \right)}} + \frac{160 \left(3 x - 7\right)^{3}}{27 \sqrt[3]{2 x + 3}}\right)}{\operatorname{atan}^{3}{\left(\frac{x}{2} \right)}}$$