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Resolución de integrales/ sin5x/ 1/(3+sin5x)

Integral de 1/(3+sin5x) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                
  /                
 |                 
 |       1         
 |  ------------ dx
 |  3 + sin(5*x)   
 |                 
/                  
0
$$\int\limits_{0}^{1} \frac{1}{\sin{\left(5 x \right)} + 3}\, dx$$ 
Integral(1/(3 + sin(5*x)), (x, 0, 1))
Respuesta (Indefinida) [src] 
                               /        /  pi   5*x\       /            ___    /5*x\\\
                               |        |- -- + ---|       |  ___   3*\/ 2 *tan|---|||
  /                        ___ |        |  2     2 |       |\/ 2               \ 2 /||
 |                       \/ 2 *|pi*floor|----------| + atan|----- + ----------------||
 |      1                      \        \    pi    /       \  4            4        //
 | ------------ dx = C + -------------------------------------------------------------
 | 3 + sin(5*x)                                        10                             
 |                                                                                    
/
$$\int \frac{1}{\sin{\left(5 x \right)} + 3}\, dx = C + \frac{\sqrt{2} \left(\operatorname{atan}{\left(\frac{3 \sqrt{2} \tan{\left(\frac{5 x}{2} \right)}}{4} + \frac{\sqrt{2}}{4} \right)} + \pi \left\lfloor{\frac{\frac{5 x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{10}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
        /          /  ___\\             /  ___       ___         \
    ___ |          |\/ 2 ||     ___     |\/ 2    3*\/ 2 *tan(5/2)|
  \/ 2 *|-pi + atan|-----||   \/ 2 *atan|----- + ----------------|
        \          \  4  //             \  4            4        /
- ------------------------- + ------------------------------------
              10                               10
$$\frac{\sqrt{2} \operatorname{atan}{\left(\frac{3 \sqrt{2} \tan{\left(\frac{5}{2} \right)}}{4} + \frac{\sqrt{2}}{4} \right)}}{10} - \frac{\sqrt{2} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{2}}{4} \right)}\right)}{10}$$ 
=
= 
        /          /  ___\\             /  ___       ___         \
    ___ |          |\/ 2 ||     ___     |\/ 2    3*\/ 2 *tan(5/2)|
  \/ 2 *|-pi + atan|-----||   \/ 2 *atan|----- + ----------------|
        \          \  4  //             \  4            4        /
- ------------------------- + ------------------------------------
              10                               10
$$\frac{\sqrt{2} \operatorname{atan}{\left(\frac{3 \sqrt{2} \tan{\left(\frac{5}{2} \right)}}{4} + \frac{\sqrt{2}}{4} \right)}}{10} - \frac{\sqrt{2} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{2}}{4} \right)}\right)}{10}$$ 
-sqrt(2)*(-pi + atan(sqrt(2)/4))/10 + sqrt(2)*atan(sqrt(2)/4 + 3*sqrt(2)*tan(5/2)/4)/10
Respuesta numérica [src] 
0.337752183007939
0.337752183007939

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

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