Общий знаменатель -log(9+x^2-3*x)/54+log(3+ ... rt(3)/3+2*x*sqrt(3)/9)/27

Вы ввели

                                             /   ___          ___\
                                     ___     |-\/ 3     2*x*\/ 3 |
    /     2      \                 \/ 3 *atan|------- + ---------|
-log\9 + x  - 3*x/    log(3 + x)             \   3          9    /
------------------- + ---------- + -------------------------------
         54               27                      27              

$$\frac{\sqrt{3}}{27} \operatorname{atan}{\left (\frac{2 x}{9} \sqrt{3} + \frac{-1 \sqrt{3}}{3} \right )} + \frac{1}{27} \log{\left (x + 3 \right )} + \frac{1}{54} \left(-1 \log{\left (- 3 x + x^{2} + 9 \right )}\right)$$

Степени

                                             /    ___         ___\
                                     ___     |  \/ 3    2*x*\/ 3 |
     /     2      \                \/ 3 *atan|- ----- + ---------|
  log\9 + x  - 3*x/   log(3 + x)             \    3         9    /
- ----------------- + ---------- + -------------------------------
          54              27                      27              

$$\frac{1}{27} \log{\left (x + 3 \right )} - \frac{1}{54} \log{\left (x^{2} - 3 x + 9 \right )} + \frac{\sqrt{3}}{27} \operatorname{atan}{\left (\frac{2 x}{9} \sqrt{3} - \frac{\sqrt{3}}{3} \right )}$$

Численный ответ

0.037037037037037*log(3 + x) + 0.0641500299099584*atan((-sqrt(3))/3 + ((2*x)*sqrt(3))/9) - 0.0185185185185185*log(9 + x^2 - 3*x)

Рациональный знаменатель

                                                 /    ___         ___\
     /     2      \                      ___     |  \/ 3    2*x*\/ 3 |
- log\9 + x  - 3*x/ + 2*log(3 + x) + 2*\/ 3 *atan|- ----- + ---------|
                                                 \    3         9    /
----------------------------------------------------------------------
                                  54                                  

$$\frac{1}{54} \left(2 \log{\left (x + 3 \right )} - \log{\left (x^{2} - 3 x + 9 \right )} + 2 \sqrt{3} \operatorname{atan}{\left (\frac{2 x}{9} \sqrt{3} - \frac{\sqrt{3}}{3} \right )}\right)$$

Объединение рациональных выражений

                                                 /  ___           \
     /     2      \                      ___     |\/ 3 *(-3 + 2*x)|
- log\9 + x  - 3*x/ + 2*log(3 + x) + 2*\/ 3 *atan|----------------|
                                                 \       9        /
-------------------------------------------------------------------
                                 54                                

$$\frac{1}{54} \left(2 \log{\left (x + 3 \right )} - \log{\left (x^{2} - 3 x + 9 \right )} + 2 \sqrt{3} \operatorname{atan}{\left (\frac{\sqrt{3}}{9} \left(2 x - 3\right) \right )}\right)$$

Общее упрощение

                                             /  ___           \
                                     ___     |\/ 3 *(-3 + 2*x)|
     /     2      \                \/ 3 *atan|----------------|
  log\9 + x  - 3*x/   log(3 + x)             \       9        /
- ----------------- + ---------- + ----------------------------
          54              27                    27             

$$\frac{1}{27} \log{\left (x + 3 \right )} - \frac{1}{54} \log{\left (x^{2} - 3 x + 9 \right )} + \frac{\sqrt{3}}{27} \operatorname{atan}{\left (\frac{\sqrt{3}}{9} \left(2 x - 3\right) \right )}$$

Собрать выражение

                                             /    ___         ___\
                                     ___     |  \/ 3    2*x*\/ 3 |
     /     2      \                \/ 3 *atan|- ----- + ---------|
  log\9 + x  - 3*x/   log(3 + x)             \    3         9    /
- ----------------- + ---------- + -------------------------------
          54              27                      27              

$$\frac{1}{27} \log{\left (x + 3 \right )} - \frac{1}{54} \log{\left (x^{2} - 3 x + 9 \right )} + \frac{\sqrt{3}}{27} \operatorname{atan}{\left (\frac{2 x}{9} \sqrt{3} - \frac{\sqrt{3}}{3} \right )}$$

Комбинаторика

                                                 /    ___         ___\
     /     2      \                      ___     |  \/ 3    2*x*\/ 3 |
- log\9 + x  - 3*x/ + 2*log(3 + x) + 2*\/ 3 *atan|- ----- + ---------|
                                                 \    3         9    /
----------------------------------------------------------------------
                                  54                                  

$$\frac{1}{54} \left(2 \log{\left (x + 3 \right )} - \log{\left (x^{2} - 3 x + 9 \right )} + 2 \sqrt{3} \operatorname{atan}{\left (\frac{2 x}{9} \sqrt{3} - \frac{\sqrt{3}}{3} \right )}\right)$$

Общий знаменатель

                                             /    ___         ___\
                                     ___     |  \/ 3    2*x*\/ 3 |
     /     2      \                \/ 3 *atan|- ----- + ---------|
  log\9 + x  - 3*x/   log(3 + x)             \    3         9    /
- ----------------- + ---------- + -------------------------------
          54              27                      27              

$$\frac{1}{27} \log{\left (x + 3 \right )} - \frac{1}{54} \log{\left (x^{2} - 3 x + 9 \right )} + \frac{\sqrt{3}}{27} \operatorname{atan}{\left (\frac{2 x}{9} \sqrt{3} - \frac{\sqrt{3}}{3} \right )}$$

Раскрыть выражение

                                             /    ___         ___\
                                     ___     |  \/ 3    2*x*\/ 3 |
     /     2      \                \/ 3 *atan|- ----- + ---------|
  log\9 + x  - 3*x/   log(3 + x)             \    3         9    /
- ----------------- + ---------- + -------------------------------
          54              27                      27              

$$\frac{1}{27} \log{\left (x + 3 \right )} - \frac{1}{54} \log{\left (x^{2} - 3 x + 9 \right )} + \frac{\sqrt{3}}{27} \operatorname{atan}{\left (\frac{2 x}{9} \sqrt{3} - \frac{\sqrt{3}}{3} \right )}$$