Общий знаменатель -6/((1+36*x^2)*(3*x^2-sqr ... ot(6*x)/(3*x^2-sqrt(x))^2
Учитель очень удивится увидев твоё верное решение😉
Решение
Вы ввели
[src]
/ 1 \
|------- - 6*x|*acot(6*x)
| ___ |
6 \2*\/ x /
- -------------------------- + -------------------------
/ 2\ / 2 ___\ 2
\1 + 36*x /*\3*x - \/ x / / 2 ___\
\3*x - \/ x /
$$\frac{\operatorname{acot}{\left (6 x \right )}}{\left(- \sqrt{x} + 3 x^{2}\right)^{2}} \left(- 6 x + \frac{1}{2 \sqrt{x}}\right) - 6 \frac{1}{\left(- \sqrt{x} + 3 x^{2}\right) \left(36 x^{2} + 1\right)}$$
Степени
[src]
/ 1 \
|------- - 6*x|*acot(6*x)
| ___ |
6 \2*\/ x /
- ---------------------------- + -------------------------
/ 2\ / ___ 2\ 2
\1 + 36*x /*\- \/ x + 3*x / / ___ 2\
\- \/ x + 3*x /
$$- \frac{6}{\left(- \sqrt{x} + 3 x^{2}\right) \left(36 x^{2} + 1\right)} + \frac{\operatorname{acot}{\left (6 x \right )}}{\left(- \sqrt{x} + 3 x^{2}\right)^{2}} \left(- 6 x + \frac{1}{2 \sqrt{x}}\right)$$
Численный ответ
[src]
-6.0/((1.0 + 36.0*x^2)*(-x^0.5 + 3.0*x^2)) + (0.5*x^(-0.5) - 6.0*x)*acot(6*x)/(-x^0.5 + 3.0*x^2)^2
Рациональный знаменатель
[src]
3 3 3 3 2 3 3 3
___ / ___ 2\ 11/2 / ___ 2\ 5/2 / ___ 2\ 7/2 / ___ 2\ ___ / ___ 2\ / ___ 2\ 2 / ___ 2\ 4 / ___ 2\
- \/ x *\\/ x + 3*x / *acot(6*x) - 1296*x *\\/ x + 3*x / *acot(6*x) - 36*x *\\/ x + 3*x / *acot(6*x) - 36*x *\\/ x + 3*x / *acot(6*x) - 12*\/ x *\\/ x - 3*x / *\\/ x + 3*x / + 15*x *\\/ x + 3*x / *acot(6*x) + 540*x *\\/ x + 3*x / *acot(6*x)
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
3
___ / 2\ / 4\
2*\/ x *\1 + 36*x /*\-x + 9*x /
$$\frac{1}{2 \sqrt{x} \left(36 x^{2} + 1\right) \left(9 x^{4} - x\right)^{3}} \left(- 1296 x^{\frac{11}{2}} \left(\sqrt{x} + 3 x^{2}\right)^{3} \operatorname{acot}{\left (6 x \right )} - 36 x^{\frac{7}{2}} \left(\sqrt{x} + 3 x^{2}\right)^{3} \operatorname{acot}{\left (6 x \right )} - 36 x^{\frac{5}{2}} \left(\sqrt{x} + 3 x^{2}\right)^{3} \operatorname{acot}{\left (6 x \right )} - 12 \sqrt{x} \left(\sqrt{x} - 3 x^{2}\right)^{2} \left(\sqrt{x} + 3 x^{2}\right)^{3} - \sqrt{x} \left(\sqrt{x} + 3 x^{2}\right)^{3} \operatorname{acot}{\left (6 x \right )} + 540 x^{4} \left(\sqrt{x} + 3 x^{2}\right)^{3} \operatorname{acot}{\left (6 x \right )} + 15 x^{2} \left(\sqrt{x} + 3 x^{2}\right)^{3} \operatorname{acot}{\left (6 x \right )}\right)$$
Объединение рациональных выражений
[src]
___ / ___ 2\ / 3/2\ / 2\
- 12*\/ x *\- \/ x + 3*x / + \1 - 12*x /*\1 + 36*x /*acot(6*x)
-----------------------------------------------------------------
2
___ / 2\ / ___ 2\
2*\/ x *\1 + 36*x /*\- \/ x + 3*x /
$$\frac{1}{2 \sqrt{x} \left(- \sqrt{x} + 3 x^{2}\right)^{2} \left(36 x^{2} + 1\right)} \left(- 12 \sqrt{x} \left(- \sqrt{x} + 3 x^{2}\right) + \left(- 12 x^{\frac{3}{2}} + 1\right) \left(36 x^{2} + 1\right) \operatorname{acot}{\left (6 x \right )}\right)$$
Общее упрощение
[src]
___ / ___ 2\ / 3/2\ / 2\
12*\/ x *\\/ x - 3*x / + \1 - 12*x /*\1 + 36*x /*acot(6*x)
-------------------------------------------------------------
2
___ / 2\ / ___ 2\
2*\/ x *\1 + 36*x /*\\/ x - 3*x /
$$\frac{1}{2 \sqrt{x} \left(\sqrt{x} - 3 x^{2}\right)^{2} \left(36 x^{2} + 1\right)} \left(12 \sqrt{x} \left(\sqrt{x} - 3 x^{2}\right) + \left(- 12 x^{\frac{3}{2}} + 1\right) \left(36 x^{2} + 1\right) \operatorname{acot}{\left (6 x \right )}\right)$$
Собрать выражение
[src]
/ 1 \
|------- - 6*x|*acot(6*x)
| ___ |
1 \2*\/ x /
- 6*-------------------------- + -------------------------
/ 2\ / 2 ___\ 2
\1 + 36*x /*\3*x - \/ x / / 2 ___\
\3*x - \/ x /
$$\frac{\operatorname{acot}{\left (6 x \right )}}{\left(- \sqrt{x} + 3 x^{2}\right)^{2}} \left(- 6 x + \frac{1}{2 \sqrt{x}}\right) - \frac{6}{\left(- \sqrt{x} + 3 x^{2}\right) \left(36 x^{2} + 1\right)}$$
Комбинаторика
[src]
5/2 7/2 3/2 2
- 36*x + 12*x - 432*x *acot(6*x) - 12*x *acot(6*x) + 36*x *acot(6*x) + acot(6*x)
---------------------------------------------------------------------------------------
2
___ / 2\ / ___ 2\
2*\/ x *\1 + 36*x /*\- \/ x + 3*x /
$$\frac{1}{2 \sqrt{x} \left(- \sqrt{x} + 3 x^{2}\right)^{2} \left(36 x^{2} + 1\right)} \left(- 432 x^{\frac{7}{2}} \operatorname{acot}{\left (6 x \right )} - 36 x^{\frac{5}{2}} - 12 x^{\frac{3}{2}} \operatorname{acot}{\left (6 x \right )} + 36 x^{2} \operatorname{acot}{\left (6 x \right )} + 12 x + \operatorname{acot}{\left (6 x \right )}\right)$$
Общий знаменатель
[src]
/ 5/2 7/2 3/2 2 \
-\- 36*x + 12*x - 432*x *acot(6*x) - 12*x *acot(6*x) + 36*x *acot(6*x) + acot(6*x)/
-------------------------------------------------------------------------------------------
13/2 7/2 9/2 3/2 3 5
- 648*x - 72*x - 18*x - 2*x + 12*x + 432*x
$$- \frac{- 432 x^{\frac{7}{2}} \operatorname{acot}{\left (6 x \right )} - 36 x^{\frac{5}{2}} - 12 x^{\frac{3}{2}} \operatorname{acot}{\left (6 x \right )} + 36 x^{2} \operatorname{acot}{\left (6 x \right )} + 12 x + \operatorname{acot}{\left (6 x \right )}}{- 648 x^{\frac{13}{2}} - 18 x^{\frac{9}{2}} - 72 x^{\frac{7}{2}} - 2 x^{\frac{3}{2}} + 432 x^{5} + 12 x^{3}}$$