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Integral de dx/(3+4*sinx) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
  1                
  /                
 |                 
 |       1         
 |  ------------ dx
 |  3 + 4*sin(x)   
 |                 
/                  
0                  
$$\int\limits_{0}^{1} \frac{1}{4 \sin{\left(x \right)} + 3}\, dx$$
Integral(1/(3 + 4*sin(x)), (x, 0, 1))
Respuesta (Indefinida) [src]
                                  /      ___         \            /      ___         \
  /                        ___    |4   \/ 7       /x\|     ___    |4   \/ 7       /x\|
 |                       \/ 7 *log|- + ----- + tan|-||   \/ 7 *log|- - ----- + tan|-||
 |      1                         \3     3        \2//            \3     3        \2//
 | ------------ dx = C - ----------------------------- + -----------------------------
 | 3 + 4*sin(x)                        7                               7              
 |                                                                                    
/                                                                                     
$$\int \frac{1}{4 \sin{\left(x \right)} + 3}\, dx = C + \frac{\sqrt{7} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{\sqrt{7}}{3} + \frac{4}{3} \right)}}{7} - \frac{\sqrt{7} \log{\left(\tan{\left(\frac{x}{2} \right)} + \frac{\sqrt{7}}{3} + \frac{4}{3} \right)}}{7}$$
Gráfica
Respuesta [src]
           /      ___\            /      ___           \            /      ___\            /      ___           \
    ___    |4   \/ 7 |     ___    |4   \/ 7            |     ___    |4   \/ 7 |     ___    |4   \/ 7            |
  \/ 7 *log|- - -----|   \/ 7 *log|- + ----- + tan(1/2)|   \/ 7 *log|- + -----|   \/ 7 *log|- - ----- + tan(1/2)|
           \3     3  /            \3     3             /            \3     3  /            \3     3             /
- -------------------- - ------------------------------- + -------------------- + -------------------------------
           7                            7                           7                            7               
$$- \frac{\sqrt{7} \log{\left(\tan{\left(\frac{1}{2} \right)} + \frac{\sqrt{7}}{3} + \frac{4}{3} \right)}}{7} + \frac{\sqrt{7} \log{\left(- \frac{\sqrt{7}}{3} + \tan{\left(\frac{1}{2} \right)} + \frac{4}{3} \right)}}{7} - \frac{\sqrt{7} \log{\left(\frac{4}{3} - \frac{\sqrt{7}}{3} \right)}}{7} + \frac{\sqrt{7} \log{\left(\frac{\sqrt{7}}{3} + \frac{4}{3} \right)}}{7}$$
=
=
           /      ___\            /      ___           \            /      ___\            /      ___           \
    ___    |4   \/ 7 |     ___    |4   \/ 7            |     ___    |4   \/ 7 |     ___    |4   \/ 7            |
  \/ 7 *log|- - -----|   \/ 7 *log|- + ----- + tan(1/2)|   \/ 7 *log|- + -----|   \/ 7 *log|- - ----- + tan(1/2)|
           \3     3  /            \3     3             /            \3     3  /            \3     3             /
- -------------------- - ------------------------------- + -------------------- + -------------------------------
           7                            7                           7                            7               
$$- \frac{\sqrt{7} \log{\left(\tan{\left(\frac{1}{2} \right)} + \frac{\sqrt{7}}{3} + \frac{4}{3} \right)}}{7} + \frac{\sqrt{7} \log{\left(- \frac{\sqrt{7}}{3} + \tan{\left(\frac{1}{2} \right)} + \frac{4}{3} \right)}}{7} - \frac{\sqrt{7} \log{\left(\frac{4}{3} - \frac{\sqrt{7}}{3} \right)}}{7} + \frac{\sqrt{7} \log{\left(\frac{\sqrt{7}}{3} + \frac{4}{3} \right)}}{7}$$
-sqrt(7)*log(4/3 - sqrt(7)/3)/7 - sqrt(7)*log(4/3 + sqrt(7)/3 + tan(1/2))/7 + sqrt(7)*log(4/3 + sqrt(7)/3)/7 + sqrt(7)*log(4/3 - sqrt(7)/3 + tan(1/2))/7
Respuesta numérica [src]
0.216442814295377
0.216442814295377

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