Sr Examen

Otras calculadoras

Resolución de integrales/ x^3-8/ (a*x^2+b*x+c)/(x^3-8)

Integral de (a*x^2+b*x+c)/(x^3-8) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                  
  /                  
 |                   
 |     2             
 |  a*x  + b*x + c   
 |  -------------- dx
 |       3           
 |      x  - 8       
 |                   
/                    
0
∫01c+(ax2+bx)x3−8 dx\int\limits_{0}^{1} \frac{c + \left(a x^{2} + b x\right)}{x^{3} - 8}\, dx 
Integral((a*x^2 + b*x + c)/(x^3 - 8), (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                                                                             /  ___        \
 |                                                    /           c\    /     2      \     ___                  |\/ 3 *(1 + x)|
 |    2                                               |-b + 4*a - -|*log\4 + x  + 2*x/   \/ 3 *(-3*c + 6*b)*atan|-------------|
 | a*x  + b*x + c          /a   b   c \               \           2/                                            \      3      /
 | -------------- dx = C + |- + - + --|*log(-2 + x) + -------------------------------- + --------------------------------------
 |      3                  \3   6   12/                              12                                    36                  
 |     x  - 8                                                                                                                  
 |                                                                                                                             
/
∫c+(ax2+bx)x3−8 dx=C+3(6b−3c)atan⁡(3(x+1)3)36+(a3+b6+c12)log⁡(x−2)+(4a−b−c2)log⁡(x2+2x+4)12\int \frac{c + \left(a x^{2} + b x\right)}{x^{3} - 8}\, dx = C + \frac{\sqrt{3} \left(6 b - 3 c\right) \operatorname{atan}{\left(\frac{\sqrt{3} \left(x + 1\right)}{3} \right)}}{36} + \left(\frac{a}{3} + \frac{b}{6} + \frac{c}{12}\right) \log{\left(x - 2 \right)} + \frac{\left(4 a - b - \frac{c}{2}\right) \log{\left(x^{2} + 2 x + 4 \right)}}{12}
Simplificar
Respuesta [src] 
                                        /                                                2                                                                                                                         \                                           /                                                2                                                                                                                         \                                           /                                            2                                                                                                                         \                                           /                                            2                                                                                                                         \                      /        2        2                      2      2                         2                         \                      /            2        2                      2      2                         2                         \
                                        |            /                    ___           \                                       /                    ___           \           /                    ___           \|                                           |            /                    ___           \                                       /                    ___           \           /                    ___           \|                                           |        /                    ___           \                                       /                    ___           \           /                    ___           \|                                           |        /                    ___           \                                       /                    ___           \           /                    ___           \|                      |- 64*b*a  - 8*a*c  - 4*b*(c + 2*b + 4*a)  + 2*c *(c + 2*b + 4*a) + 16*c*b  + 32*a*b*(c + 2*b + 4*a)|                      |    - 64*b*a  - 8*a*c  - 4*b*(c + 2*b + 4*a)  + 2*c *(c + 2*b + 4*a) + 16*c*b  + 32*a*b*(c + 2*b + 4*a)|
                                        |            |  b    c    a   I*\/ 3 *(-c + 2*b)|          2        2         2       2 |  b    c    a   I*\/ 3 *(-c + 2*b)|           |  b    c    a   I*\/ 3 *(-c + 2*b)||                                           |            |  b    c    a   I*\/ 3 *(-c + 2*b)|          2        2         2       2 |  b    c    a   I*\/ 3 *(-c + 2*b)|           |  b    c    a   I*\/ 3 *(-c + 2*b)||                                           |        |  b    c    a   I*\/ 3 *(-c + 2*b)|          2        2         2       2 |  b    c    a   I*\/ 3 *(-c + 2*b)|           |  b    c    a   I*\/ 3 *(-c + 2*b)||                                           |        |  b    c    a   I*\/ 3 *(-c + 2*b)|          2        2         2       2 |  b    c    a   I*\/ 3 *(-c + 2*b)|           |  b    c    a   I*\/ 3 *(-c + 2*b)||   (c + 2*b + 4*a)*log|---------------------------------------------------------------------------------------------------|   (c + 2*b + 4*a)*log|1 + ---------------------------------------------------------------------------------------------------|
/                    ___           \    |    - 576*b*|- -- - -- + - - ------------------|  - 64*b*a  - 8*a*c  + 16*c*b  + 24*c *|- -- - -- + - - ------------------| + 384*a*b*|- -- - -- + - - ------------------||   /                    ___           \    |    - 576*b*|- -- - -- + - + ------------------|  - 64*b*a  - 8*a*c  + 16*c*b  + 24*c *|- -- - -- + - + ------------------| + 384*a*b*|- -- - -- + - + ------------------||   /                    ___           \    |- 576*b*|- -- - -- + - - ------------------|  - 64*b*a  - 8*a*c  + 16*c*b  + 24*c *|- -- - -- + - - ------------------| + 384*a*b*|- -- - -- + - - ------------------||   /                    ___           \    |- 576*b*|- -- - -- + - + ------------------|  - 64*b*a  - 8*a*c  + 16*c*b  + 24*c *|- -- - -- + - + ------------------| + 384*a*b*|- -- - -- + - + ------------------||                      |                                               3      3                                            |                      |                                                   3      3                                            |
|  b    c    a   I*\/ 3 *(-c + 2*b)|    |            \  12   24   3           24        /                                       \  12   24   3           24        /           \  12   24   3           24        /|   |  b    c    a   I*\/ 3 *(-c + 2*b)|    |            \  12   24   3           24        /                                       \  12   24   3           24        /           \  12   24   3           24        /|   |  b    c    a   I*\/ 3 *(-c + 2*b)|    |        \  12   24   3           24        /                                       \  12   24   3           24        /           \  12   24   3           24        /|   |  b    c    a   I*\/ 3 *(-c + 2*b)|    |        \  12   24   3           24        /                                       \  12   24   3           24        /           \  12   24   3           24        /|                      \                                            - c  + 8*b                                             /                      \                                                - c  + 8*b                                             /
|- -- - -- + - - ------------------|*log|1 + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------| + |- -- - -- + - + ------------------|*log|1 + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------| - |- -- - -- + - - ------------------|*log|----------------------------------------------------------------------------------------------------------------------------------------------------------------------| - |- -- - -- + - + ------------------|*log|----------------------------------------------------------------------------------------------------------------------------------------------------------------------| - ------------------------------------------------------------------------------------------------------------------------ + ----------------------------------------------------------------------------------------------------------------------------
\  12   24   3           24        /    |                                                                                    3      3                                                                              |   \  12   24   3           24        /    |                                                                                    3      3                                                                              |   \  12   24   3           24        /    |                                                                                3      3                                                                              |   \  12   24   3           24        /    |                                                                                3      3                                                                              |                                                              12                                                                                                                           12                                                             
                                        \                                                                                 - c  + 8*b                                                                               /                                           \                                                                                 - c  + 8*b                                                                               /                                           \                                                                             - c  + 8*b                                                                               /                                           \                                                                             - c  + 8*b                                                                               /
−(4a+2b+c)log⁡(−64a2b+32ab(4a+2b+c)−8ac2+16b2c−4b(4a+2b+c)2+2c2(4a+2b+c)8b3−c3)12+(4a+2b+c)log⁡(1+−64a2b+32ab(4a+2b+c)−8ac2+16b2c−4b(4a+2b+c)2+2c2(4a+2b+c)8b3−c3)12−(a3−b12−c24−3i(2b−c)24)log⁡(−64a2b+384ab(a3−b12−c24−3i(2b−c)24)−8ac2+16b2c−576b(a3−b12−c24−3i(2b−c)24)2+24c2(a3−b12−c24−3i(2b−c)24)8b3−c3)+(a3−b12−c24−3i(2b−c)24)log⁡(1+−64a2b+384ab(a3−b12−c24−3i(2b−c)24)−8ac2+16b2c−576b(a3−b12−c24−3i(2b−c)24)2+24c2(a3−b12−c24−3i(2b−c)24)8b3−c3)−(a3−b12−c24+3i(2b−c)24)log⁡(−64a2b+384ab(a3−b12−c24+3i(2b−c)24)−8ac2+16b2c−576b(a3−b12−c24+3i(2b−c)24)2+24c2(a3−b12−c24+3i(2b−c)24)8b3−c3)+(a3−b12−c24+3i(2b−c)24)log⁡(1+−64a2b+384ab(a3−b12−c24+3i(2b−c)24)−8ac2+16b2c−576b(a3−b12−c24+3i(2b−c)24)2+24c2(a3−b12−c24+3i(2b−c)24)8b3−c3)- \frac{\left(4 a + 2 b + c\right) \log{\left(\frac{- 64 a^{2} b + 32 a b \left(4 a + 2 b + c\right) - 8 a c^{2} + 16 b^{2} c - 4 b \left(4 a + 2 b + c\right)^{2} + 2 c^{2} \left(4 a + 2 b + c\right)}{8 b^{3} - c^{3}} \right)}}{12} + \frac{\left(4 a + 2 b + c\right) \log{\left(1 + \frac{- 64 a^{2} b + 32 a b \left(4 a + 2 b + c\right) - 8 a c^{2} + 16 b^{2} c - 4 b \left(4 a + 2 b + c\right)^{2} + 2 c^{2} \left(4 a + 2 b + c\right)}{8 b^{3} - c^{3}} \right)}}{12} - \left(\frac{a}{3} - \frac{b}{12} - \frac{c}{24} - \frac{\sqrt{3} i \left(2 b - c\right)}{24}\right) \log{\left(\frac{- 64 a^{2} b + 384 a b \left(\frac{a}{3} - \frac{b}{12} - \frac{c}{24} - \frac{\sqrt{3} i \left(2 b - c\right)}{24}\right) - 8 a c^{2} + 16 b^{2} c - 576 b \left(\frac{a}{3} - \frac{b}{12} - \frac{c}{24} - \frac{\sqrt{3} i \left(2 b - c\right)}{24}\right)^{2} + 24 c^{2} \left(\frac{a}{3} - \frac{b}{12} - \frac{c}{24} - \frac{\sqrt{3} i \left(2 b - c\right)}{24}\right)}{8 b^{3} - c^{3}} \right)} + \left(\frac{a}{3} - \frac{b}{12} - \frac{c}{24} - \frac{\sqrt{3} i \left(2 b - c\right)}{24}\right) \log{\left(1 + \frac{- 64 a^{2} b + 384 a b \left(\frac{a}{3} - \frac{b}{12} - \frac{c}{24} - \frac{\sqrt{3} i \left(2 b - c\right)}{24}\right) - 8 a c^{2} + 16 b^{2} c - 576 b \left(\frac{a}{3} - \frac{b}{12} - \frac{c}{24} - \frac{\sqrt{3} i \left(2 b - c\right)}{24}\right)^{2} + 24 c^{2} \left(\frac{a}{3} - \frac{b}{12} - \frac{c}{24} - \frac{\sqrt{3} i \left(2 b - c\right)}{24}\right)}{8 b^{3} - c^{3}} \right)} - \left(\frac{a}{3} - \frac{b}{12} - \frac{c}{24} + \frac{\sqrt{3} i \left(2 b - c\right)}{24}\right) \log{\left(\frac{- 64 a^{2} b + 384 a b \left(\frac{a}{3} - \frac{b}{12} - \frac{c}{24} + \frac{\sqrt{3} i \left(2 b - c\right)}{24}\right) - 8 a c^{2} + 16 b^{2} c - 576 b \left(\frac{a}{3} - \frac{b}{12} - \frac{c}{24} + \frac{\sqrt{3} i \left(2 b - c\right)}{24}\right)^{2} + 24 c^{2} \left(\frac{a}{3} - \frac{b}{12} - \frac{c}{24} + \frac{\sqrt{3} i \left(2 b - c\right)}{24}\right)}{8 b^{3} - c^{3}} \right)} + \left(\frac{a}{3} - \frac{b}{12} - \frac{c}{24} + \frac{\sqrt{3} i \left(2 b - c\right)}{24}\right) \log{\left(1 + \frac{- 64 a^{2} b + 384 a b \left(\frac{a}{3} - \frac{b}{12} - \frac{c}{24} + \frac{\sqrt{3} i \left(2 b - c\right)}{24}\right) - 8 a c^{2} + 16 b^{2} c - 576 b \left(\frac{a}{3} - \frac{b}{12} - \frac{c}{24} + \frac{\sqrt{3} i \left(2 b - c\right)}{24}\right)^{2} + 24 c^{2} \left(\frac{a}{3} - \frac{b}{12} - \frac{c}{24} + \frac{\sqrt{3} i \left(2 b - c\right)}{24}\right)}{8 b^{3} - c^{3}} \right)} 
=
= 
                                        /                                                2                                                                                                                         \                                           /                                                2                                                                                                                         \                                           /                                            2                                                                                                                         \                                           /                                            2                                                                                                                         \                      /        2        2                      2      2                         2                         \                      /            2        2                      2      2                         2                         \
                                        |            /                    ___           \                                       /                    ___           \           /                    ___           \|                                           |            /                    ___           \                                       /                    ___           \           /                    ___           \|                                           |        /                    ___           \                                       /                    ___           \           /                    ___           \|                                           |        /                    ___           \                                       /                    ___           \           /                    ___           \|                      |- 64*b*a  - 8*a*c  - 4*b*(c + 2*b + 4*a)  + 2*c *(c + 2*b + 4*a) + 16*c*b  + 32*a*b*(c + 2*b + 4*a)|                      |    - 64*b*a  - 8*a*c  - 4*b*(c + 2*b + 4*a)  + 2*c *(c + 2*b + 4*a) + 16*c*b  + 32*a*b*(c + 2*b + 4*a)|
                                        |            |  b    c    a   I*\/ 3 *(-c + 2*b)|          2        2         2       2 |  b    c    a   I*\/ 3 *(-c + 2*b)|           |  b    c    a   I*\/ 3 *(-c + 2*b)||                                           |            |  b    c    a   I*\/ 3 *(-c + 2*b)|          2        2         2       2 |  b    c    a   I*\/ 3 *(-c + 2*b)|           |  b    c    a   I*\/ 3 *(-c + 2*b)||                                           |        |  b    c    a   I*\/ 3 *(-c + 2*b)|          2        2         2       2 |  b    c    a   I*\/ 3 *(-c + 2*b)|           |  b    c    a   I*\/ 3 *(-c + 2*b)||                                           |        |  b    c    a   I*\/ 3 *(-c + 2*b)|          2        2         2       2 |  b    c    a   I*\/ 3 *(-c + 2*b)|           |  b    c    a   I*\/ 3 *(-c + 2*b)||   (c + 2*b + 4*a)*log|---------------------------------------------------------------------------------------------------|   (c + 2*b + 4*a)*log|1 + ---------------------------------------------------------------------------------------------------|
/                    ___           \    |    - 576*b*|- -- - -- + - - ------------------|  - 64*b*a  - 8*a*c  + 16*c*b  + 24*c *|- -- - -- + - - ------------------| + 384*a*b*|- -- - -- + - - ------------------||   /                    ___           \    |    - 576*b*|- -- - -- + - + ------------------|  - 64*b*a  - 8*a*c  + 16*c*b  + 24*c *|- -- - -- + - + ------------------| + 384*a*b*|- -- - -- + - + ------------------||   /                    ___           \    |- 576*b*|- -- - -- + - - ------------------|  - 64*b*a  - 8*a*c  + 16*c*b  + 24*c *|- -- - -- + - - ------------------| + 384*a*b*|- -- - -- + - - ------------------||   /                    ___           \    |- 576*b*|- -- - -- + - + ------------------|  - 64*b*a  - 8*a*c  + 16*c*b  + 24*c *|- -- - -- + - + ------------------| + 384*a*b*|- -- - -- + - + ------------------||                      |                                               3      3                                            |                      |                                                   3      3                                            |
|  b    c    a   I*\/ 3 *(-c + 2*b)|    |            \  12   24   3           24        /                                       \  12   24   3           24        /           \  12   24   3           24        /|   |  b    c    a   I*\/ 3 *(-c + 2*b)|    |            \  12   24   3           24        /                                       \  12   24   3           24        /           \  12   24   3           24        /|   |  b    c    a   I*\/ 3 *(-c + 2*b)|    |        \  12   24   3           24        /                                       \  12   24   3           24        /           \  12   24   3           24        /|   |  b    c    a   I*\/ 3 *(-c + 2*b)|    |        \  12   24   3           24        /                                       \  12   24   3           24        /           \  12   24   3           24        /|                      \                                            - c  + 8*b                                             /                      \                                                - c  + 8*b                                             /
|- -- - -- + - - ------------------|*log|1 + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------| + |- -- - -- + - + ------------------|*log|1 + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------| - |- -- - -- + - - ------------------|*log|----------------------------------------------------------------------------------------------------------------------------------------------------------------------| - |- -- - -- + - + ------------------|*log|----------------------------------------------------------------------------------------------------------------------------------------------------------------------| - ------------------------------------------------------------------------------------------------------------------------ + ----------------------------------------------------------------------------------------------------------------------------
\  12   24   3           24        /    |                                                                                    3      3                                                                              |   \  12   24   3           24        /    |                                                                                    3      3                                                                              |   \  12   24   3           24        /    |                                                                                3      3                                                                              |   \  12   24   3           24        /    |                                                                                3      3                                                                              |                                                              12                                                                                                                           12                                                             
                                        \                                                                                 - c  + 8*b                                                                               /                                           \                                                                                 - c  + 8*b                                                                               /                                           \                                                                             - c  + 8*b                                                                               /                                           \                                                                             - c  + 8*b                                                                               /
−(4a+2b+c)log⁡(−64a2b+32ab(4a+2b+c)−8ac2+16b2c−4b(4a+2b+c)2+2c2(4a+2b+c)8b3−c3)12+(4a+2b+c)log⁡(1+−64a2b+32ab(4a+2b+c)−8ac2+16b2c−4b(4a+2b+c)2+2c2(4a+2b+c)8b3−c3)12−(a3−b12−c24−3i(2b−c)24)log⁡(−64a2b+384ab(a3−b12−c24−3i(2b−c)24)−8ac2+16b2c−576b(a3−b12−c24−3i(2b−c)24)2+24c2(a3−b12−c24−3i(2b−c)24)8b3−c3)+(a3−b12−c24−3i(2b−c)24)log⁡(1+−64a2b+384ab(a3−b12−c24−3i(2b−c)24)−8ac2+16b2c−576b(a3−b12−c24−3i(2b−c)24)2+24c2(a3−b12−c24−3i(2b−c)24)8b3−c3)−(a3−b12−c24+3i(2b−c)24)log⁡(−64a2b+384ab(a3−b12−c24+3i(2b−c)24)−8ac2+16b2c−576b(a3−b12−c24+3i(2b−c)24)2+24c2(a3−b12−c24+3i(2b−c)24)8b3−c3)+(a3−b12−c24+3i(2b−c)24)log⁡(1+−64a2b+384ab(a3−b12−c24+3i(2b−c)24)−8ac2+16b2c−576b(a3−b12−c24+3i(2b−c)24)2+24c2(a3−b12−c24+3i(2b−c)24)8b3−c3)- \frac{\left(4 a + 2 b + c\right) \log{\left(\frac{- 64 a^{2} b + 32 a b \left(4 a + 2 b + c\right) - 8 a c^{2} + 16 b^{2} c - 4 b \left(4 a + 2 b + c\right)^{2} + 2 c^{2} \left(4 a + 2 b + c\right)}{8 b^{3} - c^{3}} \right)}}{12} + \frac{\left(4 a + 2 b + c\right) \log{\left(1 + \frac{- 64 a^{2} b + 32 a b \left(4 a + 2 b + c\right) - 8 a c^{2} + 16 b^{2} c - 4 b \left(4 a + 2 b + c\right)^{2} + 2 c^{2} \left(4 a + 2 b + c\right)}{8 b^{3} - c^{3}} \right)}}{12} - \left(\frac{a}{3} - \frac{b}{12} - \frac{c}{24} - \frac{\sqrt{3} i \left(2 b - c\right)}{24}\right) \log{\left(\frac{- 64 a^{2} b + 384 a b \left(\frac{a}{3} - \frac{b}{12} - \frac{c}{24} - \frac{\sqrt{3} i \left(2 b - c\right)}{24}\right) - 8 a c^{2} + 16 b^{2} c - 576 b \left(\frac{a}{3} - \frac{b}{12} - \frac{c}{24} - \frac{\sqrt{3} i \left(2 b - c\right)}{24}\right)^{2} + 24 c^{2} \left(\frac{a}{3} - \frac{b}{12} - \frac{c}{24} - \frac{\sqrt{3} i \left(2 b - c\right)}{24}\right)}{8 b^{3} - c^{3}} \right)} + \left(\frac{a}{3} - \frac{b}{12} - \frac{c}{24} - \frac{\sqrt{3} i \left(2 b - c\right)}{24}\right) \log{\left(1 + \frac{- 64 a^{2} b + 384 a b \left(\frac{a}{3} - \frac{b}{12} - \frac{c}{24} - \frac{\sqrt{3} i \left(2 b - c\right)}{24}\right) - 8 a c^{2} + 16 b^{2} c - 576 b \left(\frac{a}{3} - \frac{b}{12} - \frac{c}{24} - \frac{\sqrt{3} i \left(2 b - c\right)}{24}\right)^{2} + 24 c^{2} \left(\frac{a}{3} - \frac{b}{12} - \frac{c}{24} - \frac{\sqrt{3} i \left(2 b - c\right)}{24}\right)}{8 b^{3} - c^{3}} \right)} - \left(\frac{a}{3} - \frac{b}{12} - \frac{c}{24} + \frac{\sqrt{3} i \left(2 b - c\right)}{24}\right) \log{\left(\frac{- 64 a^{2} b + 384 a b \left(\frac{a}{3} - \frac{b}{12} - \frac{c}{24} + \frac{\sqrt{3} i \left(2 b - c\right)}{24}\right) - 8 a c^{2} + 16 b^{2} c - 576 b \left(\frac{a}{3} - \frac{b}{12} - \frac{c}{24} + \frac{\sqrt{3} i \left(2 b - c\right)}{24}\right)^{2} + 24 c^{2} \left(\frac{a}{3} - \frac{b}{12} - \frac{c}{24} + \frac{\sqrt{3} i \left(2 b - c\right)}{24}\right)}{8 b^{3} - c^{3}} \right)} + \left(\frac{a}{3} - \frac{b}{12} - \frac{c}{24} + \frac{\sqrt{3} i \left(2 b - c\right)}{24}\right) \log{\left(1 + \frac{- 64 a^{2} b + 384 a b \left(\frac{a}{3} - \frac{b}{12} - \frac{c}{24} + \frac{\sqrt{3} i \left(2 b - c\right)}{24}\right) - 8 a c^{2} + 16 b^{2} c - 576 b \left(\frac{a}{3} - \frac{b}{12} - \frac{c}{24} + \frac{\sqrt{3} i \left(2 b - c\right)}{24}\right)^{2} + 24 c^{2} \left(\frac{a}{3} - \frac{b}{12} - \frac{c}{24} + \frac{\sqrt{3} i \left(2 b - c\right)}{24}\right)}{8 b^{3} - c^{3}} \right)} 
(-b/12 - c/24 + a/3 - i*sqrt(3)*(-c + 2*b)/24)*log(1 + (-576*b*(-b/12 - c/24 + a/3 - i*sqrt(3)*(-c + 2*b)/24)^2 - 64*b*a^2 - 8*a*c^2 + 16*c*b^2 + 24*c^2*(-b/12 - c/24 + a/3 - i*sqrt(3)*(-c + 2*b)/24) + 384*a*b*(-b/12 - c/24 + a/3 - i*sqrt(3)*(-c + 2*b)/24))/(-c^3 + 8*b^3)) + (-b/12 - c/24 + a/3 + i*sqrt(3)*(-c + 2*b)/24)*log(1 + (-576*b*(-b/12 - c/24 + a/3 + i*sqrt(3)*(-c + 2*b)/24)^2 - 64*b*a^2 - 8*a*c^2 + 16*c*b^2 + 24*c^2*(-b/12 - c/24 + a/3 + i*sqrt(3)*(-c + 2*b)/24) + 384*a*b*(-b/12 - c/24 + a/3 + i*sqrt(3)*(-c + 2*b)/24))/(-c^3 + 8*b^3)) - (-b/12 - c/24 + a/3 - i*sqrt(3)*(-c + 2*b)/24)*log((-576*b*(-b/12 - c/24 + a/3 - i*sqrt(3)*(-c + 2*b)/24)^2 - 64*b*a^2 - 8*a*c^2 + 16*c*b^2 + 24*c^2*(-b/12 - c/24 + a/3 - i*sqrt(3)*(-c + 2*b)/24) + 384*a*b*(-b/12 - c/24 + a/3 - i*sqrt(3)*(-c + 2*b)/24))/(-c^3 + 8*b^3)) - (-b/12 - c/24 + a/3 + i*sqrt(3)*(-c + 2*b)/24)*log((-576*b*(-b/12 - c/24 + a/3 + i*sqrt(3)*(-c + 2*b)/24)^2 - 64*b*a^2 - 8*a*c^2 + 16*c*b^2 + 24*c^2*(-b/12 - c/24 + a/3 + i*sqrt(3)*(-c + 2*b)/24) + 384*a*b*(-b/12 - c/24 + a/3 + i*sqrt(3)*(-c + 2*b)/24))/(-c^3 + 8*b^3)) - (c + 2*b + 4*a)*log((-64*b*a^2 - 8*a*c^2 - 4*b*(c + 2*b + 4*a)^2 + 2*c^2*(c + 2*b + 4*a) + 16*c*b^2 + 32*a*b*(c + 2*b + 4*a))/(-c^3 + 8*b^3))/12 + (c + 2*b + 4*a)*log(1 + (-64*b*a^2 - 8*a*c^2 - 4*b*(c + 2*b + 4*a)^2 + 2*c^2*(c + 2*b + 4*a) + 16*c*b^2 + 32*a*b*(c + 2*b + 4*a))/(-c^3 + 8*b^3))/12

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

    © Sr Examen – Калькулятор