Sr Examen

Otras calculadoras

Resolución de integrales/ x^2+8/ sign(8-x)/(x^2+8*x+1)

Integral de sign(8-x)/(x^2+8*x+1) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 10                
  /                
 |                 
 |  sign(8 - x)    
 |  ------------ dx
 |   2             
 |  x  + 8*x + 1   
 |                 
/                  
5
$$\int\limits_{5}^{10} \frac{\operatorname{sign}{\left(8 - x \right)}}{\left(x^{2} + 8 x\right) + 1}\, dx$$ 
Integral(sign(8 - x)/(x^2 + 8*x + 1), (x, 5, 10))
Respuesta (Indefinida) [src] 
  /                        /               
 |                        |                
 | sign(8 - x)            | sign(8 - x)    
 | ------------ dx = C +  | ------------ dx
 |  2                     |      2         
 | x  + 8*x + 1           | 1 + x  + 8*x   
 |                        |                
/                        /
$$\int \frac{\operatorname{sign}{\left(8 - x \right)}}{\left(x^{2} + 8 x\right) + 1}\, dx = C + \int \frac{\operatorname{sign}{\left(8 - x \right)}}{x^{2} + 8 x + 1}\, dx$$
Simplificar
Respuesta [src] 
    ____    /       ____\     ____    /      ____\     ____    /       ____\     ____    /       ____\     ____    /      ____\     ____    /       ____\
  \/ 15 *log\12 + \/ 15 /   \/ 15 *log\9 - \/ 15 /   \/ 15 *log\14 - \/ 15 /   \/ 15 *log\12 - \/ 15 /   \/ 15 *log\9 + \/ 15 /   \/ 15 *log\14 + \/ 15 /
- ----------------------- - ---------------------- - ----------------------- + ----------------------- + ---------------------- + -----------------------
             15                       30                        30                        15                       30                        30
$$- \frac{\sqrt{15} \log{\left(\sqrt{15} + 12 \right)}}{15} - \frac{\sqrt{15} \log{\left(14 - \sqrt{15} \right)}}{30} - \frac{\sqrt{15} \log{\left(9 - \sqrt{15} \right)}}{30} + \frac{\sqrt{15} \log{\left(\sqrt{15} + 9 \right)}}{30} + \frac{\sqrt{15} \log{\left(\sqrt{15} + 14 \right)}}{30} + \frac{\sqrt{15} \log{\left(12 - \sqrt{15} \right)}}{15}$$ 
=
= 
    ____    /       ____\     ____    /      ____\     ____    /       ____\     ____    /       ____\     ____    /      ____\     ____    /       ____\
  \/ 15 *log\12 + \/ 15 /   \/ 15 *log\9 - \/ 15 /   \/ 15 *log\14 - \/ 15 /   \/ 15 *log\12 - \/ 15 /   \/ 15 *log\9 + \/ 15 /   \/ 15 *log\14 + \/ 15 /
- ----------------------- - ---------------------- - ----------------------- + ----------------------- + ---------------------- + -----------------------
             15                       30                        30                        15                       30                        30
$$- \frac{\sqrt{15} \log{\left(\sqrt{15} + 12 \right)}}{15} - \frac{\sqrt{15} \log{\left(14 - \sqrt{15} \right)}}{30} - \frac{\sqrt{15} \log{\left(9 - \sqrt{15} \right)}}{30} + \frac{\sqrt{15} \log{\left(\sqrt{15} + 9 \right)}}{30} + \frac{\sqrt{15} \log{\left(\sqrt{15} + 14 \right)}}{30} + \frac{\sqrt{15} \log{\left(12 - \sqrt{15} \right)}}{15}$$ 
-sqrt(15)*log(12 + sqrt(15))/15 - sqrt(15)*log(9 - sqrt(15))/30 - sqrt(15)*log(14 - sqrt(15))/30 + sqrt(15)*log(12 - sqrt(15))/15 + sqrt(15)*log(9 + sqrt(15))/30 + sqrt(15)*log(14 + sqrt(15))/30
Respuesta numérica [src] 
0.0195864337106813
0.0195864337106813

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

    © Sr Examen