Sr Examen

Otras calculadoras

Resolución de integrales/ 4*x+1/ x^2-4/ (m*x-1)/(x^2-4*x+13)

Integral de (m*x-1)/(x^2-4*x+13) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                 
  /                 
 |                  
 |     m*x - 1      
 |  ------------- dx
 |   2              
 |  x  - 4*x + 13   
 |                  
/                   
0
∫01mx−1(x2−4x)+13 dx\int\limits_{0}^{1} \frac{m x - 1}{\left(x^{2} - 4 x\right) + 13}\, dx 
Integral((m*x - 1)/(x^2 - 4*x + 13), (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                           /  2   x\     /                           /  2   x\\
 |                        atan|- - + -|     |   /      2      \   2*atan|- - + -||
 |    m*x - 1                 \  3   3/     |log\13 + x  - 4*x/         \  3   3/|
 | ------------- dx = C - ------------- + m*|------------------ + ---------------|
 |  2                           3           \        2                   3       /
 | x  - 4*x + 13                                                                  
 |                                                                                
/
∫mx−1(x2−4x)+13 dx=C+m(log⁡(x2−4x+13)2+2atan⁡(x3−23)3)−atan⁡(x3−23)3\int \frac{m x - 1}{\left(x^{2} - 4 x\right) + 13}\, dx = C + m \left(\frac{\log{\left(x^{2} - 4 x + 13 \right)}}{2} + \frac{2 \operatorname{atan}{\left(\frac{x}{3} - \frac{2}{3} \right)}}{3}\right) - \frac{\operatorname{atan}{\left(\frac{x}{3} - \frac{2}{3} \right)}}{3}
Simplificar
Respuesta [src] 
/m   I*(-1 + 2*m)\    /    2 - 4*m - 3*I*(-1 + 2*m)\   /m   I*(-1 + 2*m)\    /    2 - 4*m + 3*I*(-1 + 2*m)\   /m   I*(-1 + 2*m)\    /2 - 4*m - 3*I*(-1 + 2*m)\   /m   I*(-1 + 2*m)\    /2 - 4*m + 3*I*(-1 + 2*m)\
|- - ------------|*log|1 + ------------------------| + |- + ------------|*log|1 + ------------------------| - |- - ------------|*log|------------------------| - |- + ------------|*log|------------------------|
\2        6      /    \            -1 + 2*m        /   \2        6      /    \            -1 + 2*m        /   \2        6      /    \        -1 + 2*m        /   \2        6      /    \        -1 + 2*m        /
−(m2−i(2m−1)6)log⁡(−4m−3i(2m−1)+22m−1)+(m2−i(2m−1)6)log⁡(1+−4m−3i(2m−1)+22m−1)−(m2+i(2m−1)6)log⁡(−4m+3i(2m−1)+22m−1)+(m2+i(2m−1)6)log⁡(1+−4m+3i(2m−1)+22m−1)- \left(\frac{m}{2} - \frac{i \left(2 m - 1\right)}{6}\right) \log{\left(\frac{- 4 m - 3 i \left(2 m - 1\right) + 2}{2 m - 1} \right)} + \left(\frac{m}{2} - \frac{i \left(2 m - 1\right)}{6}\right) \log{\left(1 + \frac{- 4 m - 3 i \left(2 m - 1\right) + 2}{2 m - 1} \right)} - \left(\frac{m}{2} + \frac{i \left(2 m - 1\right)}{6}\right) \log{\left(\frac{- 4 m + 3 i \left(2 m - 1\right) + 2}{2 m - 1} \right)} + \left(\frac{m}{2} + \frac{i \left(2 m - 1\right)}{6}\right) \log{\left(1 + \frac{- 4 m + 3 i \left(2 m - 1\right) + 2}{2 m - 1} \right)} 
=
= 
/m   I*(-1 + 2*m)\    /    2 - 4*m - 3*I*(-1 + 2*m)\   /m   I*(-1 + 2*m)\    /    2 - 4*m + 3*I*(-1 + 2*m)\   /m   I*(-1 + 2*m)\    /2 - 4*m - 3*I*(-1 + 2*m)\   /m   I*(-1 + 2*m)\    /2 - 4*m + 3*I*(-1 + 2*m)\
|- - ------------|*log|1 + ------------------------| + |- + ------------|*log|1 + ------------------------| - |- - ------------|*log|------------------------| - |- + ------------|*log|------------------------|
\2        6      /    \            -1 + 2*m        /   \2        6      /    \            -1 + 2*m        /   \2        6      /    \        -1 + 2*m        /   \2        6      /    \        -1 + 2*m        /
−(m2−i(2m−1)6)log⁡(−4m−3i(2m−1)+22m−1)+(m2−i(2m−1)6)log⁡(1+−4m−3i(2m−1)+22m−1)−(m2+i(2m−1)6)log⁡(−4m+3i(2m−1)+22m−1)+(m2+i(2m−1)6)log⁡(1+−4m+3i(2m−1)+22m−1)- \left(\frac{m}{2} - \frac{i \left(2 m - 1\right)}{6}\right) \log{\left(\frac{- 4 m - 3 i \left(2 m - 1\right) + 2}{2 m - 1} \right)} + \left(\frac{m}{2} - \frac{i \left(2 m - 1\right)}{6}\right) \log{\left(1 + \frac{- 4 m - 3 i \left(2 m - 1\right) + 2}{2 m - 1} \right)} - \left(\frac{m}{2} + \frac{i \left(2 m - 1\right)}{6}\right) \log{\left(\frac{- 4 m + 3 i \left(2 m - 1\right) + 2}{2 m - 1} \right)} + \left(\frac{m}{2} + \frac{i \left(2 m - 1\right)}{6}\right) \log{\left(1 + \frac{- 4 m + 3 i \left(2 m - 1\right) + 2}{2 m - 1} \right)} 
(m/2 - i*(-1 + 2*m)/6)*log(1 + (2 - 4*m - 3*i*(-1 + 2*m))/(-1 + 2*m)) + (m/2 + i*(-1 + 2*m)/6)*log(1 + (2 - 4*m + 3*i*(-1 + 2*m))/(-1 + 2*m)) - (m/2 - i*(-1 + 2*m)/6)*log((2 - 4*m - 3*i*(-1 + 2*m))/(-1 + 2*m)) - (m/2 + i*(-1 + 2*m)/6)*log((2 - 4*m + 3*i*(-1 + 2*m))/(-1 + 2*m))

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

    © Sr Examen – Калькулятор