Sr Examen

Otras calculadoras

Resolución de integrales/ i*n*x/ x^2+1/ (7x^2+1)*cos(pi*n*x)

Integral de (7x^2+1)*cos(pi*n*x) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  2                          
  /                          
 |                           
 |  /   2    \               
 |  \7*x  + 1/*cos(pi*n*x) dx
 |                           
/                            
0
∫02(7x2+1)cos⁡(xπn) dx\int\limits_{0}^{2} \left(7 x^{2} + 1\right) \cos{\left(x \pi n \right)}\, dx 
Integral((7*x^2 + 1)*cos((pi*n)*x), (x, 0, 2))
Respuesta (Indefinida) [src] 
                                      //                    3                              \                                                             
                                      ||                   x                               |                                                             
                                      ||                   --                     for n = 0|                                                             
                                      ||                   3                               |                                                             
  /                                   ||                                                   |                                                             
 |                                    ||/sin(pi*n*x)   x*cos(pi*n*x)                       |        //     x       for n = 0\   //     x       for n = 0\
 | /   2    \                         |||----------- - -------------  for n != 0           |      2 ||                      |   ||                      |
 | \7*x  + 1/*cos(pi*n*x) dx = C - 14*|<|     2  2          pi*n                           | + 7*x *|
∫(7x2+1)cos⁡(xπn) dx=C+7x2({xfor n=0sin⁡(πnx)πnotherwise)+{xfor n=0sin⁡(πnx)πnotherwise−14({x33for n=0{−xcos⁡(πnx)πn+sin⁡(πnx)π2n2for n≠00otherwiseπnotherwise)\int \left(7 x^{2} + 1\right) \cos{\left(x \pi n \right)}\, dx = C + 7 x^{2} \left(\begin{cases} x & \text{for}\: n = 0 \\\frac{\sin{\left(\pi n x \right)}}{\pi n} & \text{otherwise} \end{cases}\right) + \begin{cases} x & \text{for}\: n = 0 \\\frac{\sin{\left(\pi n x \right)}}{\pi n} & \text{otherwise} \end{cases} - 14 \left(\begin{cases} \frac{x^{3}}{3} & \text{for}\: n = 0 \\\frac{\begin{cases} - \frac{x \cos{\left(\pi n x \right)}}{\pi n} + \frac{\sin{\left(\pi n x \right)}}{\pi^{2} n^{2}} & \text{for}\: n \neq 0 \\0 & \text{otherwise} \end{cases}}{\pi n} & \text{otherwise} \end{cases}\right)
Simplificar
Respuesta [src] 
/  14*sin(2*pi*n)   28*cos(2*pi*n)   29*sin(2*pi*n)                                  
|- -------------- + -------------- + --------------  for And(n > -oo, n < oo, n != 0)
|        3  3             2  2            pi*n                                       
<      pi *n            pi *n                                                        
|                                                                                    
|                       62/3                                    otherwise            
\
{29sin⁡(2πn)πn+28cos⁡(2πn)π2n2−14sin⁡(2πn)π3n3for n>−∞∧n<∞∧n≠0623otherwise\begin{cases} \frac{29 \sin{\left(2 \pi n \right)}}{\pi n} + \frac{28 \cos{\left(2 \pi n \right)}}{\pi^{2} n^{2}} - \frac{14 \sin{\left(2 \pi n \right)}}{\pi^{3} n^{3}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\\frac{62}{3} & \text{otherwise} \end{cases} 
=
= 
/  14*sin(2*pi*n)   28*cos(2*pi*n)   29*sin(2*pi*n)                                  
|- -------------- + -------------- + --------------  for And(n > -oo, n < oo, n != 0)
|        3  3             2  2            pi*n                                       
<      pi *n            pi *n                                                        
|                                                                                    
|                       62/3                                    otherwise            
\
{29sin⁡(2πn)πn+28cos⁡(2πn)π2n2−14sin⁡(2πn)π3n3for n>−∞∧n<∞∧n≠0623otherwise\begin{cases} \frac{29 \sin{\left(2 \pi n \right)}}{\pi n} + \frac{28 \cos{\left(2 \pi n \right)}}{\pi^{2} n^{2}} - \frac{14 \sin{\left(2 \pi n \right)}}{\pi^{3} n^{3}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\\frac{62}{3} & \text{otherwise} \end{cases} 
Piecewise((-14*sin(2*pi*n)/(pi^3*n^3) + 28*cos(2*pi*n)/(pi^2*n^2) + 29*sin(2*pi*n)/(pi*n), (n > -oo)∧(n < oo)∧(Ne(n, 0))), (62/3, True))

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

    © Sr Examen – Калькулятор