Господин Экзамен
Общий знаменатель log(2*sqrt(5)*sqrt(5*x^2-1)+10*x)/sqrt(5)-sqrt(5*x^2-1)/5
Решение
Вы ввели
[src]
/ __________ \ __________
| ___ / 2 | / 2
log\2*\/ 5 *\/ 5*x - 1 + 10*x/ \/ 5*x - 1
--------------------------------- - -------------
___ 5
\/ 5
$$- \frac{\sqrt{5 x^{2} - 1}}{5} + \frac{\log{\left(10 x + 2 \sqrt{5} \sqrt{5 x^{2} - 1} \right)}}{\sqrt{5}}$$
log(2*sqrt(5)*sqrt(5*x^2 - 1*1) + 10*x)/(sqrt(5)) - sqrt(5*x^2 - 1*1)/5
Общее упрощение
[src]
___________ / ___________\
/ 2 ___ | ___ / 2 |
\/ -1 + 5*x \/ 5 *log\10*x + 2*\/ 5 *\/ -1 + 5*x /
- -------------- + ----------------------------------------
5 5
$$- \frac{\sqrt{5 x^{2} - 1}}{5} + \frac{\sqrt{5} \log{\left(10 x + 2 \sqrt{5} \sqrt{5 x^{2} - 1} \right)}}{5}$$
-sqrt(-1 + 5*x^2)/5 + sqrt(5)*log(10*x + 2*sqrt(5)*sqrt(-1 + 5*x^2))/5
Численный ответ
[src]
0.447213595499958*log(2*sqrt(5)*sqrt(5*x^2 - 1*1) + 10*x) - 0.447213595499958*(-0.2 + x^2)^0.5
0.447213595499958*log(2*sqrt(5)*sqrt(5*x^2 - 1*1) + 10*x) - 0.447213595499958*(-0.2 + x^2)^0.5
Комбинаторика
[src]
___________ / ___________\
/ 2 ___ | ___ / 2 |
\/ -1 + 5*x \/ 5 *log\10*x + 2*\/ 5 *\/ -1 + 5*x /
- -------------- + ----------------------------------------
5 5
$$- \frac{\sqrt{5 x^{2} - 1}}{5} + \frac{\sqrt{5} \log{\left(10 x + 2 \sqrt{5} \sqrt{5 x^{2} - 1} \right)}}{5}$$
-sqrt(-1 + 5*x^2)/5 + sqrt(5)*log(10*x + 2*sqrt(5)*sqrt(-1 + 5*x^2))/5
Общий знаменатель
[src]
___________ / ___________\
/ 2 ___ ___ | ___ / 2 |
\/ -1 + 5*x \/ 5 *log(2) \/ 5 *log\5*x + \/ 5 *\/ -1 + 5*x /
- -------------- + ------------ + -------------------------------------
5 5 5
$$- \frac{\sqrt{5 x^{2} - 1}}{5} + \frac{\sqrt{5} \log{\left(5 x + \sqrt{5} \sqrt{5 x^{2} - 1} \right)}}{5} + \frac{\sqrt{5} \log{\left(2 \right)}}{5}$$
-sqrt(-1 + 5*x^2)/5 + sqrt(5)*log(2)/5 + sqrt(5)*log(5*x + sqrt(5)*sqrt(-1 + 5*x^2))/5
Рациональный знаменатель
[src]
___________ / ___________\
/ 2 ___ | ___ / 2 |
- \/ -1 + 5*x + \/ 5 *log\10*x + 2*\/ 5 *\/ -1 + 5*x /
-----------------------------------------------------------
5
$$\frac{- \sqrt{5 x^{2} - 1} + \sqrt{5} \log{\left(10 x + 2 \sqrt{5} \sqrt{5 x^{2} - 1} \right)}}{5}$$
___________ / ___________\
/ 2 ___ | ___ / 2 |
\/ -1 + 5*x \/ 5 *log\10*x + 2*\/ 5 *\/ -1 + 5*x /
- -------------- + ----------------------------------------
5 5
$$- \frac{\sqrt{5 x^{2} - 1}}{5} + \frac{\sqrt{5} \log{\left(10 x + 2 \sqrt{5} \sqrt{5 x^{2} - 1} \right)}}{5}$$
-sqrt(-1 + 5*x^2)/5 + sqrt(5)*log(10*x + 2*sqrt(5)*sqrt(-1 + 5*x^2))/5
Объединение рациональных выражений
[src]
___________ / / ___________\\
/ 2 ___ | | ___ / 2 ||
- \/ -1 + 5*x + \/ 5 *log\2*\5*x + \/ 5 *\/ -1 + 5*x //
------------------------------------------------------------
5
$$\frac{- \sqrt{5 x^{2} - 1} + \sqrt{5} \log{\left(2 \cdot \left(5 x + \sqrt{5} \sqrt{5 x^{2} - 1}\right) \right)}}{5}$$
(-sqrt(-1 + 5*x^2) + sqrt(5)*log(2*(5*x + sqrt(5)*sqrt(-1 + 5*x^2))))/5
Степени
[src]
___________ / ____________ \
/ 2 ___ | / 2 |
\/ -1 + 5*x \/ 5 *log\2*\/ -5 + 25*x + 10*x/
- -------------- + -----------------------------------
5 5
$$- \frac{\sqrt{5 x^{2} - 1}}{5} + \frac{\sqrt{5} \log{\left(10 x + 2 \sqrt{25 x^{2} - 5} \right)}}{5}$$
___________ / ___________\
/ 2 ___ | ___ / 2 |
\/ -1 + 5*x \/ 5 *log\10*x + 2*\/ 5 *\/ -1 + 5*x /
- -------------- + ----------------------------------------
5 5
$$- \frac{\sqrt{5 x^{2} - 1}}{5} + \frac{\sqrt{5} \log{\left(10 x + 2 \sqrt{5} \sqrt{5 x^{2} - 1} \right)}}{5}$$
__________ / __________\
/ 2 ___ | ___ / 2 |
\/ 5*x - 1 \/ 5 *log\10*x + 2*\/ 5 *\/ 5*x - 1 /
- ------------- + ---------------------------------------
5 5
$$- \frac{\sqrt{5 x^{2} - 1}}{5} + \frac{\sqrt{5} \log{\left(10 x + 2 \sqrt{5} \sqrt{5 x^{2} - 1} \right)}}{5}$$
-sqrt(5*x^2 - 1*1)/5 + sqrt(5)*log(10*x + 2*sqrt(5)*sqrt(5*x^2 - 1*1))/5
Собрать выражение
[src]
___________ / __________ \
/ 2 ___ | ___ / 2 |
\/ -1 + 5*x \/ 5 *log\2*\/ 5 *\/ 5*x - 1 + 10*x/
- -------------- + ---------------------------------------
5 5
$$- \frac{\sqrt{5 x^{2} - 1}}{5} + \frac{\sqrt{5} \log{\left(10 x + 2 \sqrt{5} \sqrt{5 x^{2} - 1} \right)}}{5}$$
/ / 5\\
| ___________ | / ___________\ ||
___ | ___ / 2 | | ___ / 2 | ||
\/ 5 *\- \/ 5 *\/ -1 + 5*x + log\32*\5*x + \/ 5 *\/ -1 + 5*x / //
----------------------------------------------------------------------
25
$$\frac{\sqrt{5} \left(- \sqrt{5} \sqrt{5 x^{2} - 1} + \log{\left(32 \left(5 x + \sqrt{5} \sqrt{5 x^{2} - 1}\right)^{5} \right)}\right)}{25}$$
sqrt(5)*(-sqrt(5)*sqrt(-1 + 5*x^2) + log(32*(5*x + sqrt(5)*sqrt(-1 + 5*x^2))^5))/25