Sr Examen

Otras calculadoras

Resolución de integrales/ 3*x^3/ x^3+1/ 1/(3*x^3+1)

Integral de 1/(3*x^3+1) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1            
  /            
 |             
 |     1       
 |  -------- dx
 |     3       
 |  3*x  + 1   
 |             
/              
0
∫0113x3+1 dx\int\limits_{0}^{1} \frac{1}{3 x^{3} + 1}\, dx 
Integral(1/(3*x^3 + 1), (x, 0, 1))
Respuesta (Indefinida) [src] 
                             /     3 ___      2/3\             /    ___        5/6\           /     2/3\
  /                   2/3    | 2   \/ 3    x*3   |   6 ___     |  \/ 3    2*x*3   |    2/3    |    3   |
 |                   3   *log|x  + ----- - ------|   \/ 3 *atan|- ----- + --------|   3   *log|x + ----|
 |    1                      \       3       3   /             \    3        3    /           \     3  /
 | -------- dx = C - ----------------------------- + ------------------------------ + ------------------
 |    3                            18                              3                          9         
 | 3*x  + 1                                                                                             
 |                                                                                                      
/
∫13x3+1 dx=C+323log⁡(x+3233)9−323log⁡(x2−323x3+333)18+36atan⁡(2⋅356x3−33)3\int \frac{1}{3 x^{3} + 1}\, dx = C + \frac{3^{\frac{2}{3}} \log{\left(x + \frac{3^{\frac{2}{3}}}{3} \right)}}{9} - \frac{3^{\frac{2}{3}} \log{\left(x^{2} - \frac{3^{\frac{2}{3}} x}{3} + \frac{\sqrt[3]{3}}{3} \right)}}{18} + \frac{\sqrt[6]{3} \operatorname{atan}{\left(\frac{2 \cdot 3^{\frac{5}{6}} x}{3} - \frac{\sqrt{3}}{3} \right)}}{3}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.902-1
Trazar el gráfico f(x)
Respuesta [src] 
            /     5/6     ___\           / 2/3\           /     2/3   3 ___\           /     2/3\                      /3 ___\
  6 ___     |  2*3      \/ 3 |    2/3    |3   |    2/3    |    3      \/ 3 |    2/3    |    3   |               2/3    |\/ 3 |
  \/ 3 *atan|- ------ + -----|   3   *log|----|   3   *log|1 - ---- + -----|   3   *log|1 + ----|      6 ___   3   *log|-----|
            \    3        3  /           \ 3  /           \     3       3  /           \     3  /   pi*\/ 3            \  3  /
- ---------------------------- - -------------- - -------------------------- + ------------------ + -------- + ---------------
               3                       9                      18                       9               18             18
323log⁡(333)18−323log⁡(−3233+333+1)18−323log⁡(3233)9+323log⁡(3233+1)9+36π18−36atan⁡(−2⋅3563+33)3\frac{3^{\frac{2}{3}} \log{\left(\frac{\sqrt[3]{3}}{3} \right)}}{18} - \frac{3^{\frac{2}{3}} \log{\left(- \frac{3^{\frac{2}{3}}}{3} + \frac{\sqrt[3]{3}}{3} + 1 \right)}}{18} - \frac{3^{\frac{2}{3}} \log{\left(\frac{3^{\frac{2}{3}}}{3} \right)}}{9} + \frac{3^{\frac{2}{3}} \log{\left(\frac{3^{\frac{2}{3}}}{3} + 1 \right)}}{9} + \frac{\sqrt[6]{3} \pi}{18} - \frac{\sqrt[6]{3} \operatorname{atan}{\left(- \frac{2 \cdot 3^{\frac{5}{6}}}{3} + \frac{\sqrt{3}}{3} \right)}}{3} 
=
= 
            /     5/6     ___\           / 2/3\           /     2/3   3 ___\           /     2/3\                      /3 ___\
  6 ___     |  2*3      \/ 3 |    2/3    |3   |    2/3    |    3      \/ 3 |    2/3    |    3   |               2/3    |\/ 3 |
  \/ 3 *atan|- ------ + -----|   3   *log|----|   3   *log|1 - ---- + -----|   3   *log|1 + ----|      6 ___   3   *log|-----|
            \    3        3  /           \ 3  /           \     3       3  /           \     3  /   pi*\/ 3            \  3  /
- ---------------------------- - -------------- - -------------------------- + ------------------ + -------- + ---------------
               3                       9                      18                       9               18             18
323log⁡(333)18−323log⁡(−3233+333+1)18−323log⁡(3233)9+323log⁡(3233+1)9+36π18−36atan⁡(−2⋅3563+33)3\frac{3^{\frac{2}{3}} \log{\left(\frac{\sqrt[3]{3}}{3} \right)}}{18} - \frac{3^{\frac{2}{3}} \log{\left(- \frac{3^{\frac{2}{3}}}{3} + \frac{\sqrt[3]{3}}{3} + 1 \right)}}{18} - \frac{3^{\frac{2}{3}} \log{\left(\frac{3^{\frac{2}{3}}}{3} \right)}}{9} + \frac{3^{\frac{2}{3}} \log{\left(\frac{3^{\frac{2}{3}}}{3} + 1 \right)}}{9} + \frac{\sqrt[6]{3} \pi}{18} - \frac{\sqrt[6]{3} \operatorname{atan}{\left(- \frac{2 \cdot 3^{\frac{5}{6}}}{3} + \frac{\sqrt{3}}{3} \right)}}{3} 
-3^(1/6)*atan(-2*3^(5/6)/3 + sqrt(3)/3)/3 - 3^(2/3)*log(3^(2/3)/3)/9 - 3^(2/3)*log(1 - 3^(2/3)/3 + 3^(1/3)/3)/18 + 3^(2/3)*log(1 + 3^(2/3)/3)/9 + pi*3^(1/6)/18 + 3^(2/3)*log(3^(1/3)/3)/18
Respuesta numérica [src] 
0.690229424489478
0.690229424489478

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

    © Sr Examen – Калькулятор