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Integral de sinx/sin4x dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
  1            
  /            
 |             
 |   sin(x)    
 |  -------- dx
 |  sin(4*x)   
 |             
/              
0              
$$\int\limits_{0}^{1} \frac{\sin{\left(x \right)}}{\sin{\left(4 x \right)}}\, dx$$
Integral(sin(x)/sin(4*x), (x, 0, 1))
Respuesta (Indefinida) [src]
  /                              /       /x\\               /      ___      /x\\              /       ___      /x\\              /      ___      /x\\              /       ___      /x\\               /        /x\\             ___    /       /x\\             ___    /      ___      /x\\             ___    /       ___      /x\\             ___    /      ___      /x\\             ___    /       ___      /x\\             ___    /        /x\\
 |                    7761798*log|1 + tan|-||    5488420*log|1 - \/ 2  + tan|-||   5488420*log|-1 - \/ 2  + tan|-||   5488420*log|1 + \/ 2  + tan|-||   5488420*log|-1 + \/ 2  + tan|-||    7761798*log|-1 + tan|-||   5488420*\/ 2 *log|1 + tan|-||   3880899*\/ 2 *log|1 - \/ 2  + tan|-||   3880899*\/ 2 *log|-1 - \/ 2  + tan|-||   3880899*\/ 2 *log|1 + \/ 2  + tan|-||   3880899*\/ 2 *log|-1 + \/ 2  + tan|-||   5488420*\/ 2 *log|-1 + tan|-||
 |  sin(x)                       \       \2//               \               \2//              \                \2//              \               \2//              \                \2//               \        \2//                    \       \2//                    \               \2//                    \                \2//                    \               \2//                    \                \2//                    \        \2//
 | -------- dx = C - ------------------------- - ------------------------------- - -------------------------------- + ------------------------------- + -------------------------------- + ------------------------- - ----------------------------- - ------------------------------------- - -------------------------------------- + ------------------------------------- + -------------------------------------- + ------------------------------
 | sin(4*x)                                ___                            ___                               ___                                ___                               ___                             ___                           ___                                 ___                                     ___                                      ___                                     ___                                  ___   
 |                   31047192 + 21953680*\/ 2       31047192 + 21953680*\/ 2          31047192 + 21953680*\/ 2           31047192 + 21953680*\/ 2          31047192 + 21953680*\/ 2        31047192 + 21953680*\/ 2      31047192 + 21953680*\/ 2            31047192 + 21953680*\/ 2                31047192 + 21953680*\/ 2                 31047192 + 21953680*\/ 2                31047192 + 21953680*\/ 2             31047192 + 21953680*\/ 2    
/                                                                                                                                                                                                                                                                                                                                                                                                                                                      
$$\int \frac{\sin{\left(x \right)}}{\sin{\left(4 x \right)}}\, dx = C + \frac{5488420 \sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)}}{21953680 \sqrt{2} + 31047192} + \frac{7761798 \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)}}{21953680 \sqrt{2} + 31047192} - \frac{7761798 \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)}}{21953680 \sqrt{2} + 31047192} - \frac{5488420 \sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)}}{21953680 \sqrt{2} + 31047192} + \frac{5488420 \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 + \sqrt{2} \right)}}{21953680 \sqrt{2} + 31047192} + \frac{3880899 \sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 + \sqrt{2} \right)}}{21953680 \sqrt{2} + 31047192} + \frac{5488420 \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 + \sqrt{2} \right)}}{21953680 \sqrt{2} + 31047192} + \frac{3880899 \sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 + \sqrt{2} \right)}}{21953680 \sqrt{2} + 31047192} - \frac{3880899 \sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{2} - 1 \right)}}{21953680 \sqrt{2} + 31047192} - \frac{5488420 \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{2} - 1 \right)}}{21953680 \sqrt{2} + 31047192} - \frac{3880899 \sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{2} + 1 \right)}}{21953680 \sqrt{2} + 31047192} - \frac{5488420 \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{2} + 1 \right)}}{21953680 \sqrt{2} + 31047192}$$
Gráfica
Respuesta numérica [src]
-0.369220412086943
-0.369220412086943

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