Калькуляторы онлайн/ Решение уравнений/ Упрощение выражений/ -10-1/(1+x^2)-7*tan(x)^2-3*cot(x)^2+5^x*log(5) если x=1/2

-10-1/(1+x^2)-7*tan(x)^2- ... )^2+5^x*log(5) если x=1/2 (упростите выражение)

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Примеры

Решение

Вы ввели [src]
        1           2           2       x       
-10 - ------ - 7*tan (x) - 3*cot (x) + 5 *log(5)
           2                                    
      1 + x
$$5^{x} \log{\left (5 \right )} + -10 - \frac{1}{x^{2} + 1} - 7 \tan^{2}{\left (x \right )} - 3 \cot^{2}{\left (x \right )}$$
Подстановка условия [src]
-10 - 1/(1 + x^2) - 7*tan(x)^2 - 3*cot(x)^2 + 5^x*log(5) при x = 1/2
-10 - 1/(1 + x^2) - 7*tan(x)^2 - 3*cot(x)^2 + 5^x*log(5)
1 2 2 x -10- -------7*tan (x)-3*cot (x) + 5 *log(5) 2 1 + x 
-10 - 1/(1 + (1/2)^2) - 7*tan((1/2))^2 - 3*cot((1/2))^2 + 5^(1/2)*log(5)
1 2 2 (1/2) -10- -----------7*tan ((1/2))-3*cot ((1/2)) + 5 *log(5) 2 1 + (1/2) 
-10 - 1/(1 + (1/2)^2) - 7*tan(1/2)^2 - 3*cot(1/2)^2 + sqrt(5)*log(5)
1 2 2 ___ -10- -------7*tan (1/2)-3*cot (1/2) + \/ 5 *log(5) 1 1 + -- 2 2 
-48638875975601357/4503599627370496 - 7*tan(1/2)^2 - 3*cot(1/2)^2 + sqrt(5)*log(5)
$$- \frac{48638875975601357}{4503599627370496} - 3 \cot^{2}{\left (\frac{1}{2} \right )} - 7 \tan^{2}{\left (\frac{1}{2} \right )} + \sqrt{5} \log{\left (5 \right )}$$
Степени [src]
        1           2           2       x       
-10 - ------ - 7*tan (x) - 3*cot (x) + 5 *log(5)
           2                                    
      1 + x
$$5^{x} \log{\left (5 \right )} - 7 \tan^{2}{\left (x \right )} - 3 \cot^{2}{\left (x \right )} - 10 - \frac{1}{x^{2} + 1}$$
Численный ответ [src]
-10.0 - 1/(1.0 + x^2) + 1.6094379124341*5.0^x - 3.0*cot(x)^2 - 7.0*tan(x)^2
Рациональный знаменатель [src]
          2        2    /     2\        2    /     2\    x /     2\       
-11 - 10*x  - 7*tan (x)*\1 + x / - 3*cot (x)*\1 + x / + 5 *\1 + x /*log(5)
--------------------------------------------------------------------------
                                       2                                  
                                  1 + x
$$\frac{1}{x^{2} + 1} \left(5^{x} \left(x^{2} + 1\right) \log{\left (5 \right )} - 10 x^{2} - 7 \left(x^{2} + 1\right) \tan^{2}{\left (x \right )} - 3 \left(x^{2} + 1\right) \cot^{2}{\left (x \right )} - 11\right)$$
Объединение рациональных выражений [src]
          2        2    /     2\        2    /     2\    x /     2\       
-11 - 10*x  - 7*tan (x)*\1 + x / - 3*cot (x)*\1 + x / + 5 *\1 + x /*log(5)
--------------------------------------------------------------------------
                                       2                                  
                                  1 + x
$$\frac{1}{x^{2} + 1} \left(5^{x} \left(x^{2} + 1\right) \log{\left (5 \right )} - 10 x^{2} - 7 \left(x^{2} + 1\right) \tan^{2}{\left (x \right )} - 3 \left(x^{2} + 1\right) \cot^{2}{\left (x \right )} - 11\right)$$
Общее упрощение [src]
     /     2\ /     7         3       x       \
-1 + \1 + x /*|- ------- - ------- + 5 *log(5)|
              |     2         2               |
              \  cos (x)   sin (x)            /
-----------------------------------------------
                          2                    
                     1 + x
$$\frac{1}{x^{2} + 1} \left(\left(x^{2} + 1\right) \left(5^{x} \log{\left (5 \right )} - \frac{7}{\cos^{2}{\left (x \right )}} - \frac{3}{\sin^{2}{\left (x \right )}}\right) - 1\right)$$
Собрать выражение [src]
          2    x /           2       \      2    /       2\      2    /       2\
-11 - 10*x  - 5 *\-log(5) - x *log(5)/ - cot (x)*\3 + 3*x / - tan (x)*\7 + 7*x /
--------------------------------------------------------------------------------
                                          2                                     
                                     1 + x
$$\frac{1}{x^{2} + 1} \left(- 5^{x} \left(- x^{2} \log{\left (5 \right )} - \log{\left (5 \right )}\right) - 10 x^{2} - \left(3 x^{2} + 3\right) \cot^{2}{\left (x \right )} - \left(7 x^{2} + 7\right) \tan^{2}{\left (x \right )} - 11\right)$$
        1           2           2       x       
-10 - ------ - 7*tan (x) - 3*cot (x) + 5 *log(5)
           2                                    
      1 + x
$$5^{x} \log{\left (5 \right )} - 7 \tan^{2}{\left (x \right )} - 3 \cot^{2}{\left (x \right )} - 10 - \frac{1}{x^{2} + 1}$$
        1       x               2           2   
-10 - ------ + 5 *log(5) - 3*cot (x) - 7*tan (x)
           2                                    
      1 + x
$$5^{x} \log{\left (5 \right )} - 7 \tan^{2}{\left (x \right )} - 3 \cot^{2}{\left (x \right )} - 10 - \frac{1}{x^{2} + 1}$$
Комбинаторика [src]
          2        2           2       x             2    2         2    2       x  2       
-11 - 10*x  - 7*tan (x) - 3*cot (x) + 5 *log(5) - 7*x *tan (x) - 3*x *cot (x) + 5 *x *log(5)
--------------------------------------------------------------------------------------------
                                                2                                           
                                           1 + x
$$\frac{1}{x^{2} + 1} \left(5^{x} x^{2} \log{\left (5 \right )} + 5^{x} \log{\left (5 \right )} - 7 x^{2} \tan^{2}{\left (x \right )} - 3 x^{2} \cot^{2}{\left (x \right )} - 10 x^{2} - 7 \tan^{2}{\left (x \right )} - 3 \cot^{2}{\left (x \right )} - 11\right)$$
Общий знаменатель [src]
        1           2           2       x       
-10 - ------ - 7*tan (x) - 3*cot (x) + 5 *log(5)
           2                                    
      1 + x
$$5^{x} \log{\left (5 \right )} - 7 \tan^{2}{\left (x \right )} - 3 \cot^{2}{\left (x \right )} - 10 - \frac{1}{x^{2} + 1}$$
Тригонометрическая часть [src]
        1           2           2       x       
-10 - ------ - 7*tan (x) - 3*cot (x) + 5 *log(5)
           2                                    
      1 + x
$$5^{x} \log{\left (5 \right )} - 7 \tan^{2}{\left (x \right )} - 3 \cot^{2}{\left (x \right )} - 10 - \frac{1}{x^{2} + 1}$$
Раскрыть выражение [src]
        1           2           2       x       
-10 - ------ - 7*tan (x) - 3*cot (x) + 5 *log(5)
           2                                    
      1 + x
$$5^{x} \log{\left (5 \right )} - 7 \tan^{2}{\left (x \right )} - 3 \cot^{2}{\left (x \right )} - 10 - \frac{1}{x^{2} + 1}$$