Интеграл (10^x+6^x)/2^x (dx)

Вы ввели

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  1            
  /            
 |             
 |    x    x   
 |  10  + 6    
 |  -------- dx
 |      x      
 |     2       
 |             
/              
0              

$$\int_{0}^{1} \frac{1}{2^{x}} \left(10^{x} + 6^{x}\right)\, dx$$

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)
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/                                                                                                                                                                                                                                                                                                                                                                                                                          
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$${{\left(2^{{{\log 6}\over{\log 2}}}-2\right)\,\log 10+\left(2^{{{ \log 10}\over{\log 2}}}-2\right)\,\log 6+\left(-2^{{{\log 10}\over{ \log 2}}}-2^{{{\log 6}\over{\log 2}}}+4\right)\,\log 2}\over{\left(2 \,\log 6-2\,\log 2\right)\,\log 10-2\,\log 2\,\log 6+2\,\left(\log 2 \right)^2}}$$

Численный ответ

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4.30581819149212