Общий знаменатель (5*asinh((4*x+8)/(2*sqrt( ... 13))/2+sqrt(2*x^2+8*x+13)

Вы ввели

       /4*x + 8 \                                                
5*asinh|--------|        _________________                       
       |    ____|       /    2                  _________________
       \2*\/ 10 /   x*\/  2*x  + 8*x + 13      /    2            
----------------- + ---------------------- + \/  2*x  + 8*x + 13 
        3/2                   2                                  
       2                                                         

$$\frac{x}{2} \sqrt{2 x^{2} + 8 x + 13} + \frac{5}{2^{\frac{3}{2}}} \operatorname{asinh}{\left (\frac{4 x + 8}{2 \sqrt{10}} \right )} + \sqrt{2 x^{2} + 8 x + 13}$$

Степени

                                                             /  ____          \
                            _________________       ___      |\/ 10 *(8 + 4*x)|
   _________________       /         2          5*\/ 2 *asinh|----------------|
  /         2          x*\/  13 + 2*x  + 8*x                 \       20       /
\/  13 + 2*x  + 8*x  + ---------------------- + -------------------------------
                                 2                             4               

$$\frac{x}{2} \sqrt{2 x^{2} + 8 x + 13} + \sqrt{2 x^{2} + 8 x + 13} + \frac{5 \sqrt{2}}{4} \operatorname{asinh}{\left (\frac{\sqrt{10}}{20} \left(4 x + 8\right) \right )}$$

                            _________________       ___      /  ____ /2   x\\
   _________________       /         2          5*\/ 2 *asinh|\/ 10 *|- + -||
  /         2          x*\/  13 + 2*x  + 8*x                 \       \5   5//
\/  13 + 2*x  + 8*x  + ---------------------- + -----------------------------
                                 2                            4              

$$\frac{x}{2} \sqrt{2 x^{2} + 8 x + 13} + \sqrt{2 x^{2} + 8 x + 13} + \frac{5 \sqrt{2}}{4} \operatorname{asinh}{\left (\sqrt{10} \left(\frac{x}{5} + \frac{2}{5}\right) \right )}$$

Численный ответ

(13.0 + 2.0*x^2 + 8.0*x)^0.5 + 1.76776695296637*asinh((4*x + 8)/(2*sqrt(10))) + 0.5*x*(13.0 + 2.0*x^2 + 8.0*x)^0.5

Рациональный знаменатель

     _________________          _________________                /    ____       ____\
    /         2                /         2              ___      |2*\/ 10    x*\/ 10 |
4*\/  13 + 2*x  + 8*x  + 2*x*\/  13 + 2*x  + 8*x  + 5*\/ 2 *asinh|-------- + --------|
                                                                 \   5          5    /
--------------------------------------------------------------------------------------
                                          4                                           

$$\frac{1}{4} \left(2 x \sqrt{2 x^{2} + 8 x + 13} + 4 \sqrt{2 x^{2} + 8 x + 13} + 5 \sqrt{2} \operatorname{asinh}{\left (\frac{\sqrt{10} x}{5} + \frac{2 \sqrt{10}}{5} \right )}\right)$$

Объединение рациональных выражений

                                                                 /  ____        \
    __________________         __________________       ___      |\/ 10 *(2 + x)|
4*\/ 13 + 2*x*(4 + x)  + 2*x*\/ 13 + 2*x*(4 + x)  + 5*\/ 2 *asinh|--------------|
                                                                 \      5       /
---------------------------------------------------------------------------------
                                        4                                        

$$\frac{1}{4} \left(2 x \sqrt{2 x \left(x + 4\right) + 13} + 4 \sqrt{2 x \left(x + 4\right) + 13} + 5 \sqrt{2} \operatorname{asinh}{\left (\frac{\sqrt{10}}{5} \left(x + 2\right) \right )}\right)$$

Общее упрощение

                                                             /  ____        \
                            _________________       ___      |\/ 10 *(2 + x)|
   _________________       /         2          5*\/ 2 *asinh|--------------|
  /         2          x*\/  13 + 2*x  + 8*x                 \      5       /
\/  13 + 2*x  + 8*x  + ---------------------- + -----------------------------
                                 2                            4              

$$\frac{x}{2} \sqrt{2 x^{2} + 8 x + 13} + \sqrt{2 x^{2} + 8 x + 13} + \frac{5 \sqrt{2}}{4} \operatorname{asinh}{\left (\frac{\sqrt{10}}{5} \left(x + 2\right) \right )}$$

Собрать выражение

                              /4*x + 8 \                         
                       5*asinh|--------|        _________________
   _________________          |    ____|       /    2            
  /    2                      \2*\/ 10 /   x*\/  2*x  + 8*x + 13 
\/  2*x  + 8*x + 13  + ----------------- + ----------------------
                               3/2                   2           
                              2                                  

$$\frac{x}{2} \sqrt{2 x^{2} + 8 x + 13} + \sqrt{2 x^{2} + 8 x + 13} + \frac{5}{2^{\frac{3}{2}}} \operatorname{asinh}{\left (\frac{4 x + 8}{2 \sqrt{10}} \right )}$$

Комбинаторика

     _________________          _________________                /    ____       ____\
    /         2                /         2              ___      |2*\/ 10    x*\/ 10 |
4*\/  13 + 2*x  + 8*x  + 2*x*\/  13 + 2*x  + 8*x  + 5*\/ 2 *asinh|-------- + --------|
                                                                 \   5          5    /
--------------------------------------------------------------------------------------
                                          4                                           

$$\frac{1}{4} \left(2 x \sqrt{2 x^{2} + 8 x + 13} + 4 \sqrt{2 x^{2} + 8 x + 13} + 5 \sqrt{2} \operatorname{asinh}{\left (\frac{\sqrt{10} x}{5} + \frac{2 \sqrt{10}}{5} \right )}\right)$$

Общий знаменатель

                                                             /    ____       ____\
                            _________________       ___      |2*\/ 10    x*\/ 10 |
   _________________       /         2          5*\/ 2 *asinh|-------- + --------|
  /         2          x*\/  13 + 2*x  + 8*x                 \   5          5    /
\/  13 + 2*x  + 8*x  + ---------------------- + ----------------------------------
                                 2                              4                 

$$\frac{x}{2} \sqrt{2 x^{2} + 8 x + 13} + \sqrt{2 x^{2} + 8 x + 13} + \frac{5 \sqrt{2}}{4} \operatorname{asinh}{\left (\frac{\sqrt{10} x}{5} + \frac{2 \sqrt{10}}{5} \right )}$$

Раскрыть выражение

                            _________________                                  
   _________________       /    2                   ___      /  ____          \
  /    2               x*\/  2*x  + 8*x + 13      \/ 2       |\/ 10 *(4*x + 8)|
\/  2*x  + 8*x + 13  + ---------------------- + 5*-----*asinh|----------------|
                                 2                  4        \       20       /

$$\frac{x}{2} \sqrt{2 x^{2} + 8 x + 13} + \sqrt{2 x^{2} + 8 x + 13} + 5 \frac{\sqrt{2}}{4} \operatorname{asinh}{\left (\frac{\sqrt{10}}{20} \left(4 x + 8\right) \right )}$$