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Resolución de integrales/ x^2-5/ inxdx/ sin(9x^2-5)*inxdx

Integral de sin(9x^2-5)*inxdx dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                        
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 |     /   2    \          
 |  sin\9*x  - 5/*log(x) dx
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0
∫01log⁡(x)sin⁡(9x2−5) dx\int\limits_{0}^{1} \log{\left(x \right)} \sin{\left(9 x^{2} - 5 \right)}\, dx 
Integral(sin(9*x^2 - 5)*log(x), (x, 0, 1))
Respuesta (Indefinida) [src] 
                                              /                                                                                                                           \                                                                  
                                              |                          _  /              |      4\                                           _  /              |      4\|                                                                  
                                              |        ___      2       |_  |   1/4, 1/4   | -81*x |               ___  3      2              |_  |   3/4, 3/4   | -81*x ||                                                                  
                                              |  3*x*\/ 2 *Gamma (1/4)* |   |              | ------|*sin(5)   27*\/ 2 *x *Gamma (3/4)*cos(5)* |   |              | ------||                /        /      ___\    /      ___\       \       
                                   ___   ____ |                        2  3 \1/2, 5/4, 5/4 |   4   /                                         2  3 \3/2, 7/4, 7/4 |   4   /|     ___   ____ |        |3*x*\/ 2 |    |3*x*\/ 2 |       |       
  /                              \/ 2 *\/ pi *|- ---------------------------------------------------------- + ------------------------------------------------------------|   \/ 2 *\/ pi *|cos(5)*S|---------| - C|---------|*sin(5)|*log(x)
 |                                            |                         ____      2                                                   ____      2                         |                |        |    ____ |    |    ____ |       |       
 |    /   2    \                              \                    16*\/ pi *Gamma (5/4)                                         16*\/ pi *Gamma (7/4)                    /                \        \  \/ pi  /    \  \/ pi  /       /       
 | sin\9*x  - 5/*log(x) dx = C - ------------------------------------------------------------------------------------------------------------------------------------------ + ---------------------------------------------------------------
 |                                                                                                   6                                                                                                       6                               
/
∫log⁡(x)sin⁡(9x2−5) dx=C+2π(−sin⁡(5)C(32xπ)+cos⁡(5)S(32xπ))log⁡(x)6−2π(272x3cos⁡(5)Γ2(34)2F3(34,3432,74,74|−81x44)16πΓ2(74)−32xsin⁡(5)Γ2(14)2F3(14,1412,54,54|−81x44)16πΓ2(54))6\int \log{\left(x \right)} \sin{\left(9 x^{2} - 5 \right)}\, dx = C + \frac{\sqrt{2} \sqrt{\pi} \left(- \sin{\left(5 \right)} C\left(\frac{3 \sqrt{2} x}{\sqrt{\pi}}\right) + \cos{\left(5 \right)} S\left(\frac{3 \sqrt{2} x}{\sqrt{\pi}}\right)\right) \log{\left(x \right)}}{6} - \frac{\sqrt{2} \sqrt{\pi} \left(\frac{27 \sqrt{2} x^{3} \cos{\left(5 \right)} \Gamma^{2}\left(\frac{3}{4}\right) {{}_{2}F_{3}\left(\begin{matrix} \frac{3}{4}, \frac{3}{4} \\ \frac{3}{2}, \frac{7}{4}, \frac{7}{4} \end{matrix}\middle| {- \frac{81 x^{4}}{4}} \right)}}{16 \sqrt{\pi} \Gamma^{2}\left(\frac{7}{4}\right)} - \frac{3 \sqrt{2} x \sin{\left(5 \right)} \Gamma^{2}\left(\frac{1}{4}\right) {{}_{2}F_{3}\left(\begin{matrix} \frac{1}{4}, \frac{1}{4} \\ \frac{1}{2}, \frac{5}{4}, \frac{5}{4} \end{matrix}\middle| {- \frac{81 x^{4}}{4}} \right)}}{16 \sqrt{\pi} \Gamma^{2}\left(\frac{5}{4}\right)}\right)}{6}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.90-1010
Trazar el gráfico f(x)
Respuesta [src] 
              /                        _                                                                 _                         \ 
              |      ___      2       |_  /   1/4, 1/4   |      \               ___      2              |_  /   3/4, 3/4   |      \| 
              |  3*\/ 2 *Gamma (1/4)* |   |              | -81/4|*sin(5)   27*\/ 2 *Gamma (3/4)*cos(5)* |   |              | -81/4|| 
   ___   ____ |                      2  3 \1/2, 5/4, 5/4 |      /                                      2  3 \3/2, 7/4, 7/4 |      /| 
-\/ 2 *\/ pi *|- ------------------------------------------------------- + --------------------------------------------------------| 
              |                        ____      2                                               ____      2                       | 
              \                   16*\/ pi *Gamma (5/4)                                     16*\/ pi *Gamma (7/4)                  / 
-------------------------------------------------------------------------------------------------------------------------------------
                                                                  6
−2π(−32sin⁡(5)Γ2(14)2F3(14,1412,54,54|−814)16πΓ2(54)+272cos⁡(5)Γ2(34)2F3(34,3432,74,74|−814)16πΓ2(74))6- \frac{\sqrt{2} \sqrt{\pi} \left(- \frac{3 \sqrt{2} \sin{\left(5 \right)} \Gamma^{2}\left(\frac{1}{4}\right) {{}_{2}F_{3}\left(\begin{matrix} \frac{1}{4}, \frac{1}{4} \\ \frac{1}{2}, \frac{5}{4}, \frac{5}{4} \end{matrix}\middle| {- \frac{81}{4}} \right)}}{16 \sqrt{\pi} \Gamma^{2}\left(\frac{5}{4}\right)} + \frac{27 \sqrt{2} \cos{\left(5 \right)} \Gamma^{2}\left(\frac{3}{4}\right) {{}_{2}F_{3}\left(\begin{matrix} \frac{3}{4}, \frac{3}{4} \\ \frac{3}{2}, \frac{7}{4}, \frac{7}{4} \end{matrix}\middle| {- \frac{81}{4}} \right)}}{16 \sqrt{\pi} \Gamma^{2}\left(\frac{7}{4}\right)}\right)}{6} 
=
= 
              /                        _                                                                 _                         \ 
              |      ___      2       |_  /   1/4, 1/4   |      \               ___      2              |_  /   3/4, 3/4   |      \| 
              |  3*\/ 2 *Gamma (1/4)* |   |              | -81/4|*sin(5)   27*\/ 2 *Gamma (3/4)*cos(5)* |   |              | -81/4|| 
   ___   ____ |                      2  3 \1/2, 5/4, 5/4 |      /                                      2  3 \3/2, 7/4, 7/4 |      /| 
-\/ 2 *\/ pi *|- ------------------------------------------------------- + --------------------------------------------------------| 
              |                        ____      2                                               ____      2                       | 
              \                   16*\/ pi *Gamma (5/4)                                     16*\/ pi *Gamma (7/4)                  / 
-------------------------------------------------------------------------------------------------------------------------------------
                                                                  6
−2π(−32sin⁡(5)Γ2(14)2F3(14,1412,54,54|−814)16πΓ2(54)+272cos⁡(5)Γ2(34)2F3(34,3432,74,74|−814)16πΓ2(74))6- \frac{\sqrt{2} \sqrt{\pi} \left(- \frac{3 \sqrt{2} \sin{\left(5 \right)} \Gamma^{2}\left(\frac{1}{4}\right) {{}_{2}F_{3}\left(\begin{matrix} \frac{1}{4}, \frac{1}{4} \\ \frac{1}{2}, \frac{5}{4}, \frac{5}{4} \end{matrix}\middle| {- \frac{81}{4}} \right)}}{16 \sqrt{\pi} \Gamma^{2}\left(\frac{5}{4}\right)} + \frac{27 \sqrt{2} \cos{\left(5 \right)} \Gamma^{2}\left(\frac{3}{4}\right) {{}_{2}F_{3}\left(\begin{matrix} \frac{3}{4}, \frac{3}{4} \\ \frac{3}{2}, \frac{7}{4}, \frac{7}{4} \end{matrix}\middle| {- \frac{81}{4}} \right)}}{16 \sqrt{\pi} \Gamma^{2}\left(\frac{7}{4}\right)}\right)}{6} 
-sqrt(2)*sqrt(pi)*(-3*sqrt(2)*gamma(1/4)^2*hyper((1/4, 1/4), (1/2, 5/4, 5/4), -81/4)*sin(5)/(16*sqrt(pi)*gamma(5/4)^2) + 27*sqrt(2)*gamma(3/4)^2*cos(5)*hyper((3/4, 3/4), (3/2, 7/4, 7/4), -81/4)/(16*sqrt(pi)*gamma(7/4)^2))/6
Respuesta numérica [src] 
-0.652555322969425
-0.652555322969425

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

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