Интеграл (10^x+6^x)/2^x (dx)

d

↑ Введите нижнюю границу интеграла и верхнюю границу интеграла b, подинтегральную функцию f(x) - смотрите пример

    Решение

    Вы ввели
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    [text]
      1            
      /            
     |             
     |    x    x   
     |  10  + 6    
     |  -------- dx
     |      x      
     |     2       
     |             
    /              
    0              
    $$\int_{0}^{1} \frac{1}{2^{x}} \left(10^{x} + 6^{x}\right)\, dx$$
    График
    Ответ
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      1                                                                                                                                                                                                                                                                                                                                                                                                                        
      /                                                                                                                                                                                                                                                                                                                                                                                                                        
     |                                                                                                                                                                                                                                                                                                                                                                                                                         
     |    x    x                                                                                                                                                                                                                                                                                                                                                                                                               
     |  10  + 6                                  log(6)                                                       log(10)                                                          10*log(6)                                                             6*log(10)                                                          2*log(2)                                                         16*log(2)                             
     |  -------- dx = ----------------------------------------------------------- + ----------------------------------------------------------- - ------------------------------------------------------------------- - ------------------------------------------------------------------- - ----------------------------------------------------------- + -------------------------------------------------------------------
     |      x              2                                                             2                                                               2                                                                     2                                                                   2                                                               2                                                           
     |     2          - log (2) + log(2)*log(6) + log(2)*log(10) - log(6)*log(10)   - log (2) + log(2)*log(6) + log(2)*log(10) - log(6)*log(10)   - 2*log (2) - 2*log(6)*log(10) + 2*log(2)*log(6) + 2*log(2)*log(10)   - 2*log (2) - 2*log(6)*log(10) + 2*log(2)*log(6) + 2*log(2)*log(10)   - log (2) + log(2)*log(6) + log(2)*log(10) - log(6)*log(10)   - 2*log (2) - 2*log(6)*log(10) + 2*log(2)*log(6) + 2*log(2)*log(10)
     |                                                                                                                                                                                                                                                                                                                                                                                                                         
    /                                                                                                                                                                                                                                                                                                                                                                                                                          
    0                                                                                                                                                                                                                                                                                                                                                                                                                          
    $${{\left(2^{{{\log 6}\over{\log 2}}}-2\right)\,\log 10+\left(2^{{{ \log 10}\over{\log 2}}}-2\right)\,\log 6+\left(-2^{{{\log 10}\over{ \log 2}}}-2^{{{\log 6}\over{\log 2}}}+4\right)\,\log 2}\over{\left(2 \,\log 6-2\,\log 2\right)\,\log 10-2\,\log 2\,\log 6+2\,\left(\log 2 \right)^2}}$$
    Численный ответ
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    4.30581819149212