Sr Examen

Otras calculadoras

Resolución de integrales/ sin(x)/ cos(x)/ (dx)/(2*sin(x)+cos(x))

Integral de (dx)/(2*sin(x)+cos(x)) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                     
  /                     
 |                      
 |          1           
 |  ----------------- dx
 |  2*sin(x) + cos(x)   
 |                      
/                       
0
$$\int\limits_{0}^{1} \frac{1}{2 \sin{\left(x \right)} + \cos{\left(x \right)}}\, dx$$ 
Integral(1/(2*sin(x) + cos(x)), (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                             ___    /       ___      /x\\     ___    /       ___      /x\\
 |                            \/ 5 *log|-2 - \/ 5  + tan|-||   \/ 5 *log|-2 + \/ 5  + tan|-||
 |         1                           \                \2//            \                \2//
 | ----------------- dx = C - ------------------------------ + ------------------------------
 | 2*sin(x) + cos(x)                        5                                5               
 |                                                                                           
/
$$\int \frac{1}{2 \sin{\left(x \right)} + \cos{\left(x \right)}}\, dx = C + \frac{\sqrt{5} \log{\left(\tan{\left(\frac{x}{2} \right)} - 2 + \sqrt{5} \right)}}{5} - \frac{\sqrt{5} \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{5} - 2 \right)}}{5}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
    ___ /          /      ___           \\     ___    /       ___\     ___ /          /      ___\\     ___    /       ___           \
  \/ 5 *\pi*I + log\2 + \/ 5  - tan(1/2)//   \/ 5 *log\-2 + \/ 5 /   \/ 5 *\pi*I + log\2 + \/ 5 //   \/ 5 *log\-2 + \/ 5  + tan(1/2)/
- ---------------------------------------- - --------------------- + ----------------------------- + --------------------------------
                     5                                 5                           5                                5
$$\frac{\sqrt{5} \log{\left(-2 + \tan{\left(\frac{1}{2} \right)} + \sqrt{5} \right)}}{5} - \frac{\sqrt{5} \log{\left(-2 + \sqrt{5} \right)}}{5} - \frac{\sqrt{5} \left(\log{\left(- \tan{\left(\frac{1}{2} \right)} + 2 + \sqrt{5} \right)} + i \pi\right)}{5} + \frac{\sqrt{5} \left(\log{\left(2 + \sqrt{5} \right)} + i \pi\right)}{5}$$ 
=
= 
    ___ /          /      ___           \\     ___    /       ___\     ___ /          /      ___\\     ___    /       ___           \
  \/ 5 *\pi*I + log\2 + \/ 5  - tan(1/2)//   \/ 5 *log\-2 + \/ 5 /   \/ 5 *\pi*I + log\2 + \/ 5 //   \/ 5 *log\-2 + \/ 5  + tan(1/2)/
- ---------------------------------------- - --------------------- + ----------------------------- + --------------------------------
                     5                                 5                           5                                5
$$\frac{\sqrt{5} \log{\left(-2 + \tan{\left(\frac{1}{2} \right)} + \sqrt{5} \right)}}{5} - \frac{\sqrt{5} \log{\left(-2 + \sqrt{5} \right)}}{5} - \frac{\sqrt{5} \left(\log{\left(- \tan{\left(\frac{1}{2} \right)} + 2 + \sqrt{5} \right)} + i \pi\right)}{5} + \frac{\sqrt{5} \left(\log{\left(2 + \sqrt{5} \right)} + i \pi\right)}{5}$$ 
-sqrt(5)*(pi*i + log(2 + sqrt(5) - tan(1/2)))/5 - sqrt(5)*log(-2 + sqrt(5))/5 + sqrt(5)*(pi*i + log(2 + sqrt(5)))/5 + sqrt(5)*log(-2 + sqrt(5) + tan(1/2))/5
Respuesta numérica [src] 
0.597603093483765
0.597603093483765

    Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.

    © Sr Examen – Калькулятор