4 26
3 27 27*(x - 7) *acot (x)
4*(x - 7) *acot (x) - ---------------------
2
1 + x
$$- \frac{27 \left(x - 7\right)^{4} \operatorname{acot}^{26}{\left(x \right)}}{x^{2} + 1} + 4 \left(x - 7\right)^{3} \operatorname{acot}^{27}{\left(x \right)}$$
/ 2 \
2 25 | 2 36*(-7 + x)*acot(x) 9*(-7 + x) *(13 + x*acot(x))|
6*(-7 + x) *acot (x)*|2*acot (x) - ------------------- + ----------------------------|
| 2 2 |
| 1 + x / 2\ |
\ \1 + x / /
$$6 \left(x - 7\right)^{2} \left(\frac{9 \left(x - 7\right)^{2} \left(x \operatorname{acot}{\left(x \right)} + 13\right)}{\left(x^{2} + 1\right)^{2}} - \frac{36 \left(x - 7\right) \operatorname{acot}{\left(x \right)}}{x^{2} + 1} + 2 \operatorname{acot}^{2}{\left(x \right)}\right) \operatorname{acot}^{25}{\left(x \right)}$$
/ / 2 2 \ \
| 3 | 2 325 4*x *acot (x) 78*x*acot(x)| |
| 9*(-7 + x) *|- acot (x) + ------ + ------------- + ------------| |
| 2 | 2 2 2 | 2 |
24 | 3 162*acot (x)*(-7 + x) \ 1 + x 1 + x 1 + x / 108*(-7 + x) *(13 + x*acot(x))*acot(x)|
6*acot (x)*(-7 + x)*|4*acot (x) - --------------------- - ---------------------------------------------------------------- + --------------------------------------|
| 2 2 2 |
| 1 + x / 2\ / 2\ |
\ \1 + x / \1 + x / /
$$6 \left(x - 7\right) \left(- \frac{9 \left(x - 7\right)^{3} \left(\frac{4 x^{2} \operatorname{acot}^{2}{\left(x \right)}}{x^{2} + 1} + \frac{78 x \operatorname{acot}{\left(x \right)}}{x^{2} + 1} - \operatorname{acot}^{2}{\left(x \right)} + \frac{325}{x^{2} + 1}\right)}{\left(x^{2} + 1\right)^{2}} + \frac{108 \left(x - 7\right)^{2} \left(x \operatorname{acot}{\left(x \right)} + 13\right) \operatorname{acot}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{162 \left(x - 7\right) \operatorname{acot}^{2}{\left(x \right)}}{x^{2} + 1} + 4 \operatorname{acot}^{3}{\left(x \right)}\right) \operatorname{acot}^{24}{\left(x \right)}$$