Интеграл 3^x*cos(x) (dx)

Вы ввели

  1             
  /             
 |              
 |   x          
 |  3 *cos(x) dx
 |              
/               
0               

$$\int\limits_{0}^{1} 3^{x} \cos{\left(x \right)}\, dx$$

Ответ

     log(3)       3*sin(1)    3*cos(1)*log(3)
- ----------- + ----------- + ---------------
         2             2               2     
  1 + log (3)   1 + log (3)     1 + log (3)  

$$- \frac{\log{\left(3 \right)}}{1 + \log{\left(3 \right)}^{2}} + \frac{3 \log{\left(3 \right)} \cos{\left(1 \right)}}{1 + \log{\left(3 \right)}^{2}} + \frac{3 \sin{\left(1 \right)}}{1 + \log{\left(3 \right)}^{2}}$$

=

=

     log(3)       3*sin(1)    3*cos(1)*log(3)
- ----------- + ----------- + ---------------
         2             2               2     
  1 + log (3)   1 + log (3)     1 + log (3)  

$$- \frac{\log{\left(3 \right)}}{1 + \log{\left(3 \right)}^{2}} + \frac{3 \log{\left(3 \right)} \cos{\left(1 \right)}}{1 + \log{\left(3 \right)}^{2}} + \frac{3 \sin{\left(1 \right)}}{1 + \log{\left(3 \right)}^{2}}$$

Численный ответ

1.45293297722767

Ответ (Неопределённый)

  /                                                 
 |                      x            x              
 |  x                  3 *sin(x)    3 *cos(x)*log(3)
 | 3 *cos(x) dx = C + ----------- + ----------------
 |                           2               2      
/                     1 + log (3)     1 + log (3)   

$$\int 3^{x} \cos{\left(x \right)}\, dx = \frac{3^{x} \sin{\left(x \right)}}{1 + \log{\left(3 \right)}^{2}} + \frac{3^{x} \log{\left(3 \right)} \cos{\left(x \right)}}{1 + \log{\left(3 \right)}^{2}} + C$$

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