Sr Examen

Otras calculadoras

Resolución de integrales/ (x^2)/ x+x^2/ sqrt4x/ dx/(x^2)sqrt4x+x^2

Integral de dx/(x^2)sqrt4x+x^2 dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                  
  /                  
 |                   
 |  /  _____     \   
 |  |\/ 4*x     2|   
 |  |------- + x | dx
 |  |    2       |   
 |  \   x        /   
 |                   
/                    
0
∫01(4xx2+x2) dx\int\limits_{0}^{1} \left(\frac{\sqrt{4 x}}{x^{2}} + x^{2}\right)\, dx 
Integral(sqrt(4*x)/x^2 + x^2, (x, 0, 1))
Solución detallada

  1. Integramos término a término:

    1. No puedo encontrar los pasos en la búsqueda de esta integral.

      Pero la integral

      {−4xfor ∣x∣>1∨∣x∣<12G2,21,1(112−120|x)+2G2,20,2(12,1−12,0|x)otherwese\begin{cases} - \frac{4}{\sqrt{x}} & \text{for}\: \left|{x}\right| > 1 \vee \left|{x}\right| < 1 \\2 {G_{2, 2}^{1, 1}\left(\begin{matrix} 1 & \frac{1}{2} \\- \frac{1}{2} & 0 \end{matrix} \middle| {x} \right)} + 2 {G_{2, 2}^{0, 2}\left(\begin{matrix} \frac{1}{2}, 1 & \\ & - \frac{1}{2}, 0 \end{matrix} \middle| {x} \right)} & \text{otherwese} \end{cases}

    1. Integral xnx^{n} es xn+1n+1\frac{x^{n + 1}}{n + 1} when n≠−1n \neq -1:

      ∫x2 dx=x33\int x^{2}\, dx = \frac{x^{3}}{3}

    El resultado es: x33+{−4xfor ∣x∣>1∨∣x∣<12G2,21,1(112−120|x)+2G2,20,2(12,1−12,0|x)otherwese\frac{x^{3}}{3} + \begin{cases} - \frac{4}{\sqrt{x}} & \text{for}\: \left|{x}\right| > 1 \vee \left|{x}\right| < 1 \\2 {G_{2, 2}^{1, 1}\left(\begin{matrix} 1 & \frac{1}{2} \\- \frac{1}{2} & 0 \end{matrix} \middle| {x} \right)} + 2 {G_{2, 2}^{0, 2}\left(\begin{matrix} \frac{1}{2}, 1 & \\ & - \frac{1}{2}, 0 \end{matrix} \middle| {x} \right)} & \text{otherwese} \end{cases}

  2. Ahora simplificar:

    {x33−4xfor ∣x∣≠1x33+2G2,21,1(112−120|x)+2G2,20,2(12,1−12,0|x)otherwese\begin{cases} \frac{x^{3}}{3} - \frac{4}{\sqrt{x}} & \text{for}\: \left|{x}\right| \neq 1 \\\frac{x^{3}}{3} + 2 {G_{2, 2}^{1, 1}\left(\begin{matrix} 1 & \frac{1}{2} \\- \frac{1}{2} & 0 \end{matrix} \middle| {x} \right)} + 2 {G_{2, 2}^{0, 2}\left(\begin{matrix} \frac{1}{2}, 1 & \\ & - \frac{1}{2}, 0 \end{matrix} \middle| {x} \right)} & \text{otherwese} \end{cases}

  3. Añadimos la constante de integración:

    {x33−4xfor ∣x∣≠1x33+2G2,21,1(112−120|x)+2G2,20,2(12,1−12,0|x)otherwese+constant\begin{cases} \frac{x^{3}}{3} - \frac{4}{\sqrt{x}} & \text{for}\: \left|{x}\right| \neq 1 \\\frac{x^{3}}{3} + 2 {G_{2, 2}^{1, 1}\left(\begin{matrix} 1 & \frac{1}{2} \\- \frac{1}{2} & 0 \end{matrix} \middle| {x} \right)} + 2 {G_{2, 2}^{0, 2}\left(\begin{matrix} \frac{1}{2}, 1 & \\ & - \frac{1}{2}, 0 \end{matrix} \middle| {x} \right)} & \text{otherwese} \end{cases}+ \mathrm{constant}

Respuesta:

{x33−4xfor ∣x∣≠1x33+2G2,21,1(112−120|x)+2G2,20,2(12,1−12,0|x)otherwese+constant\begin{cases} \frac{x^{3}}{3} - \frac{4}{\sqrt{x}} & \text{for}\: \left|{x}\right| \neq 1 \\\frac{x^{3}}{3} + 2 {G_{2, 2}^{1, 1}\left(\begin{matrix} 1 & \frac{1}{2} \\- \frac{1}{2} & 0 \end{matrix} \middle| {x} \right)} + 2 {G_{2, 2}^{0, 2}\left(\begin{matrix} \frac{1}{2}, 1 & \\ & - \frac{1}{2}, 0 \end{matrix} \middle| {x} \right)} & \text{otherwese} \end{cases}+ \mathrm{constant}

Respuesta (Indefinida) [src] 
  /                             //                            -4                                                       \
 |                              ||                           -----                             for Or(|x| > 1, |x| < 1)|
 | /  _____     \           3   ||                             ___                                                     |
 | |\/ 4*x     2|          x    ||                           \/ x                                                      |
 | |------- + x | dx = C + -- + |<                                                                                     |
 | |    2       |          3    ||   __1, 1 / 1    1/2 |  \      __0, 2 /1/2, 1          |  \                          |
 | \   x        /               ||2*/__     |          | x| + 2*/__     |                | x|         otherwise        |
 |                              ||  \_|2, 2 \-1/2   0  |  /     \_|2, 2 \        -1/2, 0 |  /                          |
/                               \\                                                                                     /
∫(4xx2+x2) dx=C+x33+{−4xfor ∣x∣>1∨∣x∣<12G2,21,1(112−120|x)+2G2,20,2(12,1−12,0|x)otherwise\int \left(\frac{\sqrt{4 x}}{x^{2}} + x^{2}\right)\, dx = C + \frac{x^{3}}{3} + \begin{cases} - \frac{4}{\sqrt{x}} & \text{for}\: \left|{x}\right| > 1 \vee \left|{x}\right| < 1 \\2 {G_{2, 2}^{1, 1}\left(\begin{matrix} 1 & \frac{1}{2} \\- \frac{1}{2} & 0 \end{matrix} \middle| {x} \right)} + 2 {G_{2, 2}^{0, 2}\left(\begin{matrix} \frac{1}{2}, 1 & \\ & - \frac{1}{2}, 0 \end{matrix} \middle| {x} \right)} & \text{otherwise} \end{cases}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.90-20000002000000
Trazar el gráfico f(x)
Respuesta [src] 
oo
∞\infty 
=
= 
oo
∞\infty 
oo
Respuesta numérica [src] 
14928897195.6463
14928897195.6463

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

    © Sr Examen – Калькулятор