Господин Экзамен
Упрощение выражений/
Общий знаменатель/
-6/((1+36*x^2)*(3*x^2-sqrt(x)))+(1/(2*sqrt(x))-6*x)*acot(6*x)/(3*x^2-sqrt(x))^2
Общий знаменатель -6/((1+36*x^2)*(3*x^2-sqrt(x)))+(1/(2*sqrt(x))-6*x)*acot(6*x)/(3*x^2-sqrt(x))^2
Решение
Вы ввели
[src]
/ 1 \
|1*------- - 6*x|*acot(6*x)
| ___ |
6 \ 2*\/ x /
- -------------------------- + ---------------------------
/ 2\ / 2 ___\ 2
\1 + 36*x /*\3*x - \/ x / / 2 ___\
\3*x - \/ x /
$$\frac{\left(- 6 x + 1 \cdot \frac{1}{2 \sqrt{x}}\right) \operatorname{acot}{\left(6 x \right)}}{\left(3 x^{2} - \sqrt{x}\right)^{2}} - \frac{6}{\left(3 x^{2} - \sqrt{x}\right) \left(36 x^{2} + 1\right)}$$
-6*1/((1 + 36*x^2)*(3*x^2 - sqrt(x))) + (1/(2*sqrt(x)) - 6*x)*acot(6*x)/((3*x^2 - sqrt(x))^2)
Общее упрощение
[src]
___ / ___ 2\ / 2\ / 3/2\
12*\/ x *\\/ x - 3*x / - \1 + 36*x /*\-1 + 12*x /*acot(6*x)
--------------------------------------------------------------
2
___ / 2\ / ___ 2\
2*\/ x *\1 + 36*x /*\\/ x - 3*x /
$$\frac{- \left(12 x^{\frac{3}{2}} - 1\right) \left(36 x^{2} + 1\right) \operatorname{acot}{\left(6 x \right)} + 12 \sqrt{x} \left(- 3 x^{2} + \sqrt{x}\right)}{2 \sqrt{x} \left(- 3 x^{2} + \sqrt{x}\right)^{2} \cdot \left(36 x^{2} + 1\right)}$$
(12*sqrt(x)*(sqrt(x) - 3*x^2) - (1 + 36*x^2)*(-1 + 12*x^(3/2))*acot(6*x))/(2*sqrt(x)*(1 + 36*x^2)*(sqrt(x) - 3*x^2)^2)
Рациональный знаменатель
[src]
6 acot(6*x) 6*x*acot(6*x)
- --------------------------------- + ------------------------- - -----------------
___ 5/2 2 4 2 2
- \/ x - 36*x + 3*x + 108*x ___ / ___ 2\ / ___ 2\
2*\/ x *\- \/ x + 3*x / \- \/ x + 3*x /
$$- \frac{6 x \operatorname{acot}{\left(6 x \right)}}{\left(3 x^{2} - \sqrt{x}\right)^{2}} - \frac{6}{- 36 x^{\frac{5}{2}} + 108 x^{4} + 3 x^{2} - \sqrt{x}} + \frac{\operatorname{acot}{\left(6 x \right)}}{2 \sqrt{x} \left(3 x^{2} - \sqrt{x}\right)^{2}}$$
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 /
$$\frac{- 1296 x^{\frac{11}{2}} \left(3 x^{2} + \sqrt{x}\right)^{3} \operatorname{acot}{\left(6 x \right)} - 36 x^{\frac{7}{2}} \left(3 x^{2} + \sqrt{x}\right)^{3} \operatorname{acot}{\left(6 x \right)} - 36 x^{\frac{5}{2}} \left(3 x^{2} + \sqrt{x}\right)^{3} \operatorname{acot}{\left(6 x \right)} + 540 x^{4} \left(3 x^{2} + \sqrt{x}\right)^{3} \operatorname{acot}{\left(6 x \right)} - 12 \sqrt{x} \left(- 3 x^{2} + \sqrt{x}\right)^{2} \left(3 x^{2} + \sqrt{x}\right)^{3} + 15 x^{2} \left(3 x^{2} + \sqrt{x}\right)^{3} \operatorname{acot}{\left(6 x \right)} - \sqrt{x} \left(3 x^{2} + \sqrt{x}\right)^{3} \operatorname{acot}{\left(6 x \right)}}{2 \sqrt{x} \left(36 x^{2} + 1\right) \left(9 x^{4} - x\right)^{3}}$$
(-sqrt(x)*(sqrt(x) + 3*x^2)^3*acot(6*x) - 1296*x^(11/2)*(sqrt(x) + 3*x^2)^3*acot(6*x) - 36*x^(5/2)*(sqrt(x) + 3*x^2)^3*acot(6*x) - 36*x^(7/2)*(sqrt(x) + 3*x^2)^3*acot(6*x) - 12*sqrt(x)*(sqrt(x) - 3*x^2)^2*(sqrt(x) + 3*x^2)^3 + 15*x^2*(sqrt(x) + 3*x^2)^3*acot(6*x) + 540*x^4*(sqrt(x) + 3*x^2)^3*acot(6*x))/(2*sqrt(x)*(1 + 36*x^2)*(-x + 9*x^4)^3)
Собрать выражение
[src]
/ 1 \
|------- - 6*x|*acot(6*x)
| ___ |
6 \2*\/ x /
- ---------------------------- + -------------------------
/ 2\ / ___ 2\ 2
\1 + 36*x /*\- \/ x + 3*x / / ___ 2\
\- \/ x + 3*x /
$$\frac{\left(- 6 x + \frac{1}{2 \sqrt{x}}\right) \operatorname{acot}{\left(6 x \right)}}{\left(3 x^{2} - \sqrt{x}\right)^{2}} - \frac{6}{\left(3 x^{2} - \sqrt{x}\right) \left(36 x^{2} + 1\right)}$$
-6/((1 + 36*x^2)*(-sqrt(x) + 3*x^2)) + (1/(2*sqrt(x)) - 6*x)*acot(6*x)/(-sqrt(x) + 3*x^2)^2
Общий знаменатель
[src]
5/2 2 3/2 7/2
-acot(6*x) - 12*x + 36*x - 36*x *acot(6*x) + 12*x *acot(6*x) + 432*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
$$\frac{432 x^{\frac{7}{2}} \operatorname{acot}{\left(6 x \right)} + 36 x^{\frac{5}{2}} + 12 x^{\frac{3}{2}} \operatorname{acot}{\left(6 x \right)} - 36 x^{2} \operatorname{acot}{\left(6 x \right)} - 12 x - \operatorname{acot}{\left(6 x \right)}}{- 648 x^{\frac{13}{2}} - 18 x^{\frac{9}{2}} - 72 x^{\frac{7}{2}} + 432 x^{5} - 2 x^{\frac{3}{2}} + 12 x^{3}}$$
(-acot(6*x) - 12*x + 36*x^(5/2) - 36*x^2*acot(6*x) + 12*x^(3/2)*acot(6*x) + 432*x^(7/2)*acot(6*x))/(-648*x^(13/2) - 72*x^(7/2) - 18*x^(9/2) - 2*x^(3/2) + 12*x^3 + 432*x^5)
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 /
$$\frac{\left(- 12 x^{\frac{3}{2}} + 1\right) \left(36 x^{2} + 1\right) \operatorname{acot}{\left(6 x \right)} - 12 \sqrt{x} \left(3 x^{2} - \sqrt{x}\right)}{2 \sqrt{x} \left(3 x^{2} - \sqrt{x}\right)^{2} \cdot \left(36 x^{2} + 1\right)}$$
(-12*sqrt(x)*(-sqrt(x) + 3*x^2) + (1 - 12*x^(3/2))*(1 + 36*x^2)*acot(6*x))/(2*sqrt(x)*(1 + 36*x^2)*(-sqrt(x) + 3*x^2)^2)
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 /
$$\frac{- 432 x^{\frac{7}{2}} \operatorname{acot}{\left(6 x \right)} - 36 x^{\frac{5}{2}} - 12 x^{\frac{3}{2}} \operatorname{acot}{\left(6 x \right)} + 36 x^{2} \operatorname{acot}{\left(6 x \right)} + 12 x + \operatorname{acot}{\left(6 x \right)}}{2 \sqrt{x} \left(3 x^{2} - \sqrt{x}\right)^{2} \cdot \left(36 x^{2} + 1\right)}$$
(-36*x^(5/2) + 12*x - 432*x^(7/2)*acot(6*x) - 12*x^(3/2)*acot(6*x) + 36*x^2*acot(6*x) + acot(6*x))/(2*sqrt(x)*(1 + 36*x^2)*(-sqrt(x) + 3*x^2)^2)
Степени
[src]
/ 1 \
|------- - 6*x|*acot(6*x)
| ___ |
6 \2*\/ x /
- ---------------------------- + -------------------------
/ 2\ / ___ 2\ 2
\1 + 36*x /*\- \/ x + 3*x / / ___ 2\
\- \/ x + 3*x /
$$\frac{\left(- 6 x + \frac{1}{2 \sqrt{x}}\right) \operatorname{acot}{\left(6 x \right)}}{\left(3 x^{2} - \sqrt{x}\right)^{2}} - \frac{6}{\left(3 x^{2} - \sqrt{x}\right) \left(36 x^{2} + 1\right)}$$
/ 1 \
|------- - 6*x|*acot(6*x)
| ___ |
6 \2*\/ x /
- -------------------------- + -------------------------
/ 2\ / 2 ___\ 2
\1 + 36*x /*\3*x - \/ x / / 2 ___\
\3*x - \/ x /
$$\frac{\left(- 6 x + \frac{1}{2 \sqrt{x}}\right) \operatorname{acot}{\left(6 x \right)}}{\left(3 x^{2} - \sqrt{x}\right)^{2}} - \frac{6}{\left(3 x^{2} - \sqrt{x}\right) \left(36 x^{2} + 1\right)}$$
-6/((1 + 36*x^2)*(3*x^2 - sqrt(x))) + (1/(2*sqrt(x)) - 6*x)*acot(6*x)/(3*x^2 - sqrt(x))^2
Тригонометрическая часть
[src]
___ / ___ 2\ / 2\ / 3/2\
12*\/ x *\\/ x - 3*x / - \1 + 36*x /*\-1 + 12*x /*acot(6*x)
--------------------------------------------------------------
2
___ / 2\ / ___ 2\
2*\/ x *\1 + 36*x /*\\/ x - 3*x /
$$\frac{- \left(12 x^{\frac{3}{2}} - 1\right) \left(36 x^{2} + 1\right) \operatorname{acot}{\left(6 x \right)} + 12 \sqrt{x} \left(- 3 x^{2} + \sqrt{x}\right)}{2 \sqrt{x} \left(- 3 x^{2} + \sqrt{x}\right)^{2} \cdot \left(36 x^{2} + 1\right)}$$
(12*sqrt(x)*(sqrt(x) - 3*x^2) - (1 + 36*x^2)*(-1 + 12*x^(3/2))*acot(6*x))/(2*sqrt(x)*(1 + 36*x^2)*(sqrt(x) - 3*x^2)^2)
Численный ответ
[src]
-6.0/((1.0 + 36.0*x^2)*(-x^0.5 + 3.0*x^2)) + 0.111111111111111*(0.5/x^0.5 - 6.0*x)*acot(6*x)/(x^2 - 0.333333333333333*x^0.5)^2
-6.0/((1.0 + 36.0*x^2)*(-x^0.5 + 3.0*x^2)) + 0.111111111111111*(0.5/x^0.5 - 6.0*x)*acot(6*x)/(x^2 - 0.333333333333333*x^0.5)^2