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Resolución de integrales/ 4-x^2/ x/2+1/ cosx// 3*cosx/ (x^3*cosx/2+1/2)sqrt/4-x^2

Integral de (x^3*cosx/2+1/2)sqrt/4-x^2 dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  2                                
  /                                
 |                                 
 |  // 3           \           \   
 |  ||x *cos(x)   1|   ___     |   
 |  ||--------- + -|*\/ x      |   
 |  |\    2       2/          2|   
 |  |--------------------- - x | dx
 |  \          4               /   
 |                                 
/                                  
-2
∫−22(−x2+x(x3cos⁡(x)2+12)4) dx\int\limits_{-2}^{2} \left(- x^{2} + \frac{\sqrt{x} \left(\frac{x^{3} \cos{\left(x \right)}}{2} + \frac{1}{2}\right)}{4}\right)\, dx 
Integral((((x^3*cos(x))/2 + 1/2)*sqrt(x))/4 - x^2, (x, -2, 2))
Respuesta (Indefinida) [src] 
  /                                                                                                                                                                                                                                                                                                                  
 |                                                                /        /  ___   ___\                     /  ___   ___\                                                                                                                                                         \                    /  ___   ___\
 | // 3           \           \                                   |        |\/ 2 *\/ x |                  4  |\/ 2 *\/ x |                                                                                                                                                         |     ___   ____  4  |\/ 2 *\/ x |
 | ||x *cos(x)   1|   ___     |                                   |  4725*C|-----------|*Gamma(1/4)   45*x *C|-----------|*Gamma(1/4)                                                                                                                                              |   \/ 2 *\/ pi *x *C|-----------|
 | ||--------- + -|*\/ x      |           3    3/2                |        |     ____  |                     |     ____  |                    ___  5/2                          ___  7/2                            ___  3/2                            ___   ___                  |                    |     ____  |
 | |\    2       2/          2|          x    x        ___   ____ |        \   \/ pi   /                     \   \/ pi   /              315*\/ 2 *x   *cos(x)*Gamma(1/4)   45*\/ 2 *x   *Gamma(1/4)*sin(x)   1575*\/ 2 *x   *Gamma(1/4)*sin(x)   4725*\/ 2 *\/ x *cos(x)*Gamma(1/4)|                    \   \/ pi   /
 | |--------------------- - x | dx = C - -- + ---- - \/ 2 *\/ pi *|- ------------------------------ + ------------------------------- - -------------------------------- - ------------------------------- + --------------------------------- + ----------------------------------| + ------------------------------
 | \          4               /          3     12                 |         8192*Gamma(13/4)                  512*Gamma(13/4)                      ____                               ____                               ____                                ____                  |                 8               
 |                                                                \                                                                         2048*\/ pi *Gamma(13/4)            1024*\/ pi *Gamma(13/4)            4096*\/ pi *Gamma(13/4)             8192*\/ pi *Gamma(13/4)      /                                 
/
∫(−x2+x(x3cos⁡(x)2+12)4) dx=C+x3212+2πx4C(2xπ)8−x33−2π(−452x72sin⁡(x)Γ(14)1024πΓ(134)−3152x52cos⁡(x)Γ(14)2048πΓ(134)+15752x32sin⁡(x)Γ(14)4096πΓ(134)+47252xcos⁡(x)Γ(14)8192πΓ(134)+45x4C(2xπ)Γ(14)512Γ(134)−4725C(2xπ)Γ(14)8192Γ(134))\int \left(- x^{2} + \frac{\sqrt{x} \left(\frac{x^{3} \cos{\left(x \right)}}{2} + \frac{1}{2}\right)}{4}\right)\, dx = C + \frac{x^{\frac{3}{2}}}{12} + \frac{\sqrt{2} \sqrt{\pi} x^{4} C\left(\frac{\sqrt{2} \sqrt{x}}{\sqrt{\pi}}\right)}{8} - \frac{x^{3}}{3} - \sqrt{2} \sqrt{\pi} \left(- \frac{45 \sqrt{2} x^{\frac{7}{2}} \sin{\left(x \right)} \Gamma\left(\frac{1}{4}\right)}{1024 \sqrt{\pi} \Gamma\left(\frac{13}{4}\right)} - \frac{315 \sqrt{2} x^{\frac{5}{2}} \cos{\left(x \right)} \Gamma\left(\frac{1}{4}\right)}{2048 \sqrt{\pi} \Gamma\left(\frac{13}{4}\right)} + \frac{1575 \sqrt{2} x^{\frac{3}{2}} \sin{\left(x \right)} \Gamma\left(\frac{1}{4}\right)}{4096 \sqrt{\pi} \Gamma\left(\frac{13}{4}\right)} + \frac{4725 \sqrt{2} \sqrt{x} \cos{\left(x \right)} \Gamma\left(\frac{1}{4}\right)}{8192 \sqrt{\pi} \Gamma\left(\frac{13}{4}\right)} + \frac{45 x^{4} C\left(\frac{\sqrt{2} \sqrt{x}}{\sqrt{\pi}}\right) \Gamma\left(\frac{1}{4}\right)}{512 \Gamma\left(\frac{13}{4}\right)} - \frac{4725 C\left(\frac{\sqrt{2} \sqrt{x}}{\sqrt{\pi}}\right) \Gamma\left(\frac{1}{4}\right)}{8192 \Gamma\left(\frac{13}{4}\right)}\right)
Simplificar
Respuesta numérica [src] 
(-5.14038347943263 + 0.277889429944293j)
(-5.14038347943263 + 0.277889429944293j)

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

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