Господин Экзамен
Общий знаменатель (2*atan(sqrt(e^x-5)/sqrt(5)))/(sqrt(5)*log(e))
Решение
Вы ввели
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/ ________\
| / x |
|\/ e - 5 |
2*atan|-----------|
| ___ |
\ \/ 5 /
-------------------
___
\/ 5 *log(e)
$$\frac{2 \operatorname{atan}{\left(\frac{\sqrt{e^{x} - 5}}{\sqrt{5}} \right)}}{\sqrt{5} \log{\left(e \right)}}$$
2*atan(sqrt(E^x - 1*5)/(sqrt(5)))/((sqrt(5)*log(E)))
Общее упрощение
[src]
/ _________\
| ___ / x |
___ |\/ 5 *\/ -5 + e |
2*\/ 5 *atan|------------------|
\ 5 /
--------------------------------
5
$$\frac{2 \sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \sqrt{e^{x} - 5}}{5} \right)}}{5}$$
2*sqrt(5)*atan(sqrt(5)*sqrt(-5 + exp(x))/5)/5
Разложение дроби
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2*sqrt(5)*atan(sqrt(5)*sqrt(-5 + exp(x))/5)/5
$$\frac{2 \sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \sqrt{e^{x} - 5}}{5} \right)}}{5}$$
/ _________\
| ___ / x |
___ |\/ 5 *\/ -5 + e |
2*\/ 5 *atan|------------------|
\ 5 /
--------------------------------
5
Собрать выражение
[src]
/ _________\
| ___ / x |
___ |\/ 5 *\/ -5 + e |
2*\/ 5 *atan|------------------|
\ 5 /
--------------------------------
5
$$\frac{2 \sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \sqrt{e^{x} - 5}}{5} \right)}}{5}$$
/ ________\
| / x |
___ |\/ e - 5 |
2*\/ 5 *atan|-----------|
| ___ |
\ \/ 5 /
-------------------------
5*log(e)
$$\frac{2 \sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{e^{x} - 5}}{\sqrt{5}} \right)}}{5 \log{\left(e \right)}}$$
2*sqrt(5)*atan(sqrt(E^x - 1*5)/(sqrt(5)))/(5*log(E))
Численный ответ
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0.894427190999916*atan(sqrt(E^x - 1*5)/(sqrt(5)))
0.894427190999916*atan(sqrt(E^x - 1*5)/(sqrt(5)))
Рациональный знаменатель
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/ _________\
| ___ / x |
___ |\/ 5 *\/ -5 + e |
2*\/ 5 *atan|------------------|
\ 5 /
--------------------------------
5
$$\frac{2 \sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \sqrt{e^{x} - 5}}{5} \right)}}{5}$$
2*sqrt(5)*atan(sqrt(5)*sqrt(-5 + exp(x))/5)/5
Объединение рациональных выражений
[src]
/ _________\
| ___ / x |
___ |\/ 5 *\/ -5 + e |
2*\/ 5 *atan|------------------|
\ 5 /
--------------------------------
5
$$\frac{2 \sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \sqrt{e^{x} - 5}}{5} \right)}}{5}$$
2*sqrt(5)*atan(sqrt(5)*sqrt(-5 + exp(x))/5)/5
Степени
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/ ____________\
| / x |
___ |\/ -25 + 5*e |
2*\/ 5 *atan|---------------|
\ 5 /
-----------------------------
5
$$\frac{2 \sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5 e^{x} - 25}}{5} \right)}}{5}$$
/ _________\
| ___ / x |
___ |\/ 5 *\/ -5 + e |
2*\/ 5 *atan|------------------|
\ 5 /
--------------------------------
5
$$\frac{2 \sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \sqrt{e^{x} - 5}}{5} \right)}}{5}$$
/ _________\
| ___ / x |
___ |\/ 5 *\/ -5 + e |
2*\/ 5 *atan|------------------|
\ 5 /
--------------------------------
5*log(e)
$$\frac{2 \sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \sqrt{e^{x} - 5}}{5} \right)}}{5 \log{\left(e \right)}}$$
/ ________\
| ___ / x |
___ |\/ 5 *\/ e - 5 |
2*\/ 5 *atan|-----------------|
\ 5 /
-------------------------------
5*log(e)
$$\frac{2 \sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \sqrt{e^{x} - 5}}{5} \right)}}{5 \log{\left(e \right)}}$$
2*sqrt(5)*atan(sqrt(5)*sqrt(E^x - 1*5)/5)/(5*log(E))
Тригонометрическая часть
[src]
/ ___ \
___ | \/ 5 |
2*\/ 5 *acot|------------|
| _________|
| / x |
\\/ -5 + e /
--------------------------
5
$$\frac{2 \sqrt{5} \operatorname{acot}{\left(\frac{\sqrt{5}}{\sqrt{e^{x} - 5}} \right)}}{5}$$
/ _________\
| ___ / x |
___ |\/ 5 *\/ -5 + e |
2*\/ 5 *atan|------------------|
\ 5 /
--------------------------------
5
$$\frac{2 \sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \sqrt{e^{x} - 5}}{5} \right)}}{5}$$
___ / _________ ___\ \/ 5 | / x \/ 5 | 2*--------*atan|\/ -5 + e *-----| 5*log(e) \ 5 /
$$2 \frac{\sqrt{5}}{5 \log{\left(e \right)}} \operatorname{atan}{\left(\frac{\sqrt{5}}{5} \sqrt{e^{x} - 5} \right)}$$
/ _________\
| ___ / x |
___ |\/ 5 *\/ -5 + e |
2*\/ 5 *atan|------------------|
\ 5 /
--------------------------------
5*log(e)
$$\frac{2 \sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \sqrt{e^{x} - 5}}{5} \right)}}{5 \log{\left(e \right)}}$$
/ ___ ________________________\
___ |\/ 5 *\/ -5 + cosh(x) + sinh(x) |
2*\/ 5 *atan|--------------------------------|
\ 5 /
----------------------------------------------
5
$$\frac{2 \sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \sqrt{\sinh{\left(x \right)} + \cosh{\left(x \right)} - 5}}{5} \right)}}{5}$$
/ ___ ________________________\
___ |\/ 5 *\/ -5 + cosh(x) + sinh(x) |
2*\/ 5 *atan|--------------------------------|
\ 5 /
----------------------------------------------
5*log(cosh(1) + sinh(1))
$$\frac{2 \sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \sqrt{\sinh{\left(x \right)} + \cosh{\left(x \right)} - 5}}{5} \right)}}{5 \log{\left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)} \right)}}$$
2*sqrt(5)*atan(sqrt(5)*sqrt(-5 + cosh(x) + sinh(x))/5)/(5*log(cosh(1) + sinh(1)))
Общий знаменатель
[src]
/ _________\
| ___ / x |
___ |\/ 5 *\/ -5 + e |
2*\/ 5 *atan|------------------|
\ 5 /
--------------------------------
5
$$\frac{2 \sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \sqrt{e^{x} - 5}}{5} \right)}}{5}$$
2*sqrt(5)*atan(sqrt(5)*sqrt(-5 + exp(x))/5)/5
Комбинаторика
[src]
/ _________\
| ___ / x |
___ |\/ 5 *\/ -5 + e |
2*\/ 5 *atan|------------------|
\ 5 /
--------------------------------
5
$$\frac{2 \sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \sqrt{e^{x} - 5}}{5} \right)}}{5}$$
2*sqrt(5)*atan(sqrt(5)*sqrt(-5 + exp(x))/5)/5