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Resolución de integrales/ (x+1)/ sin5x/ sqrt(x)/ (sqrt(x)+sqrt(x+1))sin5x

Integral de (sqrt(x)+sqrt(x+1))sin5x dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 oo                                
  /                                
 |                                 
 |  /  ___     _______\            
 |  \\/ x  + \/ x + 1 /*sin(5*x) dx
 |                                 
/                                  
0
∫0∞(x+x+1)sin⁡(5x) dx\int\limits_{0}^{\infty} \left(\sqrt{x} + \sqrt{x + 1}\right) \sin{\left(5 x \right)}\, dx 
Integral((sqrt(x) + sqrt(x + 1))*sin(5*x), (x, 0, oo))
Respuesta (Indefinida) [src] 
                                                         /                                                                                                                                                                           \                                                                                                                                                                                 
                                                         |                                            _  /              |            2\                                                             _  /              |            2\|                                                                                                                                                                                 
                                                         |    ____        3/2                        |_  |   1/4, 3/4   | -25*(1 + x) |              ____        5/2                               |_  |   3/4, 5/4   | -25*(1 + x) ||                                                                                                                                                                                 
                                                         |  \/ 10 *(1 + x)   *Gamma(1/4)*Gamma(3/4)* |   |              | ------------|*sin(5)   5*\/ 10 *(1 + x)   *cos(5)*Gamma(3/4)*Gamma(5/4)* |   |              | ------------||                    /  ____   ___\                         /        /  ____   _______\    /  ____   _______\       \                                                             
                                             ____   ____ |                                          2  3 \1/2, 5/4, 7/4 |      4      /                                                           2  3 \3/2, 7/4, 9/4 |      4      /|       ____   ____  |\/ 10 *\/ x |     ____   ____         |        |\/ 10 *\/ 1 + x |    |\/ 10 *\/ 1 + x |       |                                  _  /              |      2\
  /                                      2*\/ 10 *\/ pi *|- ---------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------|   x*\/ 10 *\/ pi *S|------------|   \/ 10 *\/ pi *(1 + x)*|cos(5)*S|----------------| - C|----------------|*sin(5)|      5/2                        |_  |   3/4, 5/4   | -25*x |
 |                                                       |                                ____                                                                                  ____                                                 |                    |     ____   |                         |        |       ____     |    |       ____     |       |   5*x   *Gamma(3/4)*Gamma(5/4)* |   |              | ------|
 | /  ___     _______\                                   \                           16*\/ pi *Gamma(5/4)*Gamma(7/4)                                                       16*\/ pi *Gamma(7/4)*Gamma(9/4)                           /                    \   \/ pi    /                         \        \     \/ pi      /    \     \/ pi      /       /                                2  3 \3/2, 7/4, 9/4 |   4   /
 | \\/ x  + \/ x + 1 /*sin(5*x) dx = C - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------- + ------------------------------------------------------------------------------- - ----------------------------------------------------------
 |                                                                                                                                     5                                                                                                                5                                                         5                                                           4*Gamma(7/4)*Gamma(9/4)                  
/
∫(x+x+1)sin⁡(5x) dx=C−5x52Γ(34)Γ(54)2F3(34,5432,74,94|−25x24)4Γ(74)Γ(94)+10πxS(10xπ)5+10π(x+1)(−sin⁡(5)C(10x+1π)+cos⁡(5)S(10x+1π))5−210π(510(x+1)52cos⁡(5)Γ(34)Γ(54)2F3(34,5432,74,94|−25(x+1)24)16πΓ(74)Γ(94)−10(x+1)32sin⁡(5)Γ(14)Γ(34)2F3(14,3412,54,74|−25(x+1)24)16πΓ(54)Γ(74))5\int \left(\sqrt{x} + \sqrt{x + 1}\right) \sin{\left(5 x \right)}\, dx = C - \frac{5 x^{\frac{5}{2}} \Gamma\left(\frac{3}{4}\right) \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{3}\left(\begin{matrix} \frac{3}{4}, \frac{5}{4} \\ \frac{3}{2}, \frac{7}{4}, \frac{9}{4} \end{matrix}\middle| {- \frac{25 x^{2}}{4}} \right)}}{4 \Gamma\left(\frac{7}{4}\right) \Gamma\left(\frac{9}{4}\right)} + \frac{\sqrt{10} \sqrt{\pi} x S\left(\frac{\sqrt{10} \sqrt{x}}{\sqrt{\pi}}\right)}{5} + \frac{\sqrt{10} \sqrt{\pi} \left(x + 1\right) \left(- \sin{\left(5 \right)} C\left(\frac{\sqrt{10} \sqrt{x + 1}}{\sqrt{\pi}}\right) + \cos{\left(5 \right)} S\left(\frac{\sqrt{10} \sqrt{x + 1}}{\sqrt{\pi}}\right)\right)}{5} - \frac{2 \sqrt{10} \sqrt{\pi} \left(\frac{5 \sqrt{10} \left(x + 1\right)^{\frac{5}{2}} \cos{\left(5 \right)} \Gamma\left(\frac{3}{4}\right) \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{3}\left(\begin{matrix} \frac{3}{4}, \frac{5}{4} \\ \frac{3}{2}, \frac{7}{4}, \frac{9}{4} \end{matrix}\middle| {- \frac{25 \left(x + 1\right)^{2}}{4}} \right)}}{16 \sqrt{\pi} \Gamma\left(\frac{7}{4}\right) \Gamma\left(\frac{9}{4}\right)} - \frac{\sqrt{10} \left(x + 1\right)^{\frac{3}{2}} \sin{\left(5 \right)} \Gamma\left(\frac{1}{4}\right) \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{3}\left(\begin{matrix} \frac{1}{4}, \frac{3}{4} \\ \frac{1}{2}, \frac{5}{4}, \frac{7}{4} \end{matrix}\middle| {- \frac{25 \left(x + 1\right)^{2}}{4}} \right)}}{16 \sqrt{\pi} \Gamma\left(\frac{5}{4}\right) \Gamma\left(\frac{7}{4}\right)}\right)}{5}
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    Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.

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