________
30*\/ -9 + x
-------------
/ ________\ x
\270 - 15*x + x*\/ -9 + x /*e
------------------------------------------
________
x*\/ -9 + x
$$\frac{\left(x \sqrt{x - 9} - 15 x + 270\right) e^{\frac{30 \sqrt{x - 9}}{x}}}{x \sqrt{x - 9}}$$
(270 - 15*x + x*sqrt(-9 + x))*exp(30*sqrt(-9 + x)/x)/(x*sqrt(-9 + x))
Рациональный знаменатель
[src]
________ ________
30*\/ -9 + x 30*\/ -9 + x ________
------------- ------------- 30*\/ -9 + x
x ________ x -------------
15*e 30*\/ -9 + x *e x
----------------- - ---------------------------- + e
________ x
\/ -9 + x
$$e^{\frac{30 \sqrt{x - 9}}{x}} - \frac{30 \sqrt{x - 9} e^{\frac{30 \sqrt{x - 9}}{x}}}{x} + \frac{15 e^{\frac{30 \sqrt{x - 9}}{x}}}{\sqrt{x - 9}}$$
________ ________ ________
30*\/ -9 + x 30*\/ -9 + x 30*\/ -9 + x
------------- ------------- -------------
3 x 2 x 3 ________ x
- 15*x *e + 270*x *e + x *\/ -9 + x *e
-----------------------------------------------------------------------------
3 ________
x *\/ -9 + x
$$\frac{x^{3} \sqrt{x - 9} e^{\frac{30 \sqrt{x - 9}}{x}} - 15 x^{3} e^{\frac{30 \sqrt{x - 9}}{x}} + 270 x^{2} e^{\frac{30 \sqrt{x - 9}}{x}}}{x^{3} \sqrt{x - 9}}$$
(-15*x^3*exp(30*sqrt(-9 + x)/x) + 270*x^2*exp(30*sqrt(-9 + x)/x) + x^3*sqrt(-9 + x)*exp(30*sqrt(-9 + x)/x))/(x^3*sqrt(-9 + x))
Тригонометрическая часть
[src]
________
30*\/ -9 + x
-------------
/ ________\ x
\270 - 15*x + x*\/ -9 + x /*e
------------------------------------------
________
x*\/ -9 + x
$$\frac{\left(x \sqrt{x - 9} - 15 x + 270\right) e^{\frac{30 \sqrt{x - 9}}{x}}}{x \sqrt{x - 9}}$$
________
30*\/ -9 + x ________
------------- 30*\/ -9 + x
/ 2 \ x -------------
15*\x - 2*x*(-9 + x)/*e x
------------------------------------- + e
2 ________
x *\/ -9 + x
$$e^{\frac{30 \sqrt{x - 9}}{x}} + \frac{15 \left(x^{2} - 2 x \left(x - 9\right)\right) e^{\frac{30 \sqrt{x - 9}}{x}}}{x^{2} \sqrt{x - 9}}$$
/ ________ \ / / ________\ / ________\\ / ________\ / ________\
| 30*\/ -9 + x 15 | | |30*\/ -9 + x | |30*\/ -9 + x || |30*\/ -9 + x | |30*\/ -9 + x |
x*|- ------------- + ------------|*|cosh|-------------| + sinh|-------------|| + cosh|-------------| + sinh|-------------|
| 2 ________| \ \ x / \ x // \ x / \ x /
\ x x*\/ -9 + x /
$$x \left(- \frac{30 \sqrt{x - 9}}{x^{2}} + \frac{15}{x \sqrt{x - 9}}\right) \left(\sinh{\left(\frac{30 \sqrt{x - 9}}{x} \right)} + \cosh{\left(\frac{30 \sqrt{x - 9}}{x} \right)}\right) + \sinh{\left(\frac{30 \sqrt{x - 9}}{x} \right)} + \cosh{\left(\frac{30 \sqrt{x - 9}}{x} \right)}$$
x*(-30*sqrt(-9 + x)/x^2 + 15/(x*sqrt(-9 + x)))*(cosh(30*sqrt(-9 + x)/x) + sinh(30*sqrt(-9 + x)/x)) + cosh(30*sqrt(-9 + x)/x) + sinh(30*sqrt(-9 + x)/x)
Объединение рациональных выражений
[src]
________
30*\/ -9 + x
-------------
/ ________\ x
\270 - 15*x + x*\/ -9 + x /*e
------------------------------------------
________
x*\/ -9 + x
$$\frac{\left(x \sqrt{x - 9} - 15 x + 270\right) e^{\frac{30 \sqrt{x - 9}}{x}}}{x \sqrt{x - 9}}$$
(270 - 15*x + x*sqrt(-9 + x))*exp(30*sqrt(-9 + x)/x)/(x*sqrt(-9 + x))
________
30*\/ -9 + x
-------------
/ ________\ x
\270 - 15*x + x*\/ -9 + x /*e
------------------------------------------
________
x*\/ -9 + x
$$\frac{\left(x \sqrt{x - 9} - 15 x + 270\right) e^{\frac{30 \sqrt{x - 9}}{x}}}{x \sqrt{x - 9}}$$
(270 - 15*x + x*sqrt(-9 + x))*exp(30*sqrt(-9 + x)/x)/(x*sqrt(-9 + x))
________ ________
30*\/ -9 + x 30*\/ -9 + x ________
------------- ------------- 30*\/ -9 + x
x x -------------
270*e - 15*x*e x
---------------------------------------- + e
________
x*\/ -9 + x
$$e^{\frac{30 \sqrt{x - 9}}{x}} + \frac{- 15 x e^{\frac{30 \sqrt{x - 9}}{x}} + 270 e^{\frac{30 \sqrt{x - 9}}{x}}}{x \sqrt{x - 9}}$$
(270*exp(30*sqrt(-9 + x)/x) - 15*x*exp(30*sqrt(-9 + x)/x))/(x*sqrt(-9 + x)) + exp(30*sqrt(-9 + x)/x)