Sr Examen
Integral de e^(6/x^3) dx
Solución
Ha introducido
[src]
1 / | | 6 | -- | 3 | x | E dx | / 0
$$\int\limits_{0}^{1} e^{\frac{6}{x^{3}}}\, dx$$
Integral(E^(6/x^3), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ -2*pi*I | ------- / pi*I pi*I\ | 6 3 ___ 3 |e 6*e | | -- \/ 6 *e *Gamma(-1/3)*lowergamma|-----, -------| | 3 | 3 3 | | x \ x / | E dx = C - ----------------------------------------------------- | 9*Gamma(2/3) /
$$\int e^{\frac{6}{x^{3}}}\, dx = C - \frac{\sqrt[3]{6} e^{- \frac{2 i \pi}{3}} \Gamma\left(- \frac{1}{3}\right) \gamma\left(\frac{e^{i \pi}}{3}, \frac{6 e^{i \pi}}{x^{3}}\right)}{9 \Gamma\left(\frac{2}{3}\right)}$$
Respuesta
[src]
-2*pi*I -2*pi*I
------- / pi*I \ ------- / pi*I \
3 ___ 3 |e pi*I| 3 ___ 3 |e |
\/ 6 *e *Gamma(-1/3)*lowergamma|-----, 6*e | \/ 6 *e *Gamma(-1/3)*lowergamma|-----, -oo|
\ 3 / \ 3 /
- ----------------------------------------------------- + -------------------------------------------------
9*Gamma(2/3) 9*Gamma(2/3)
-2*pi*I -2*pi*I
------- / pi*I \ ------- / pi*I \
3 ___ 3 |e pi*I| 3 ___ 3 |e |
\/ 6 *e *Gamma(-1/3)*lowergamma|-----, 6*e | \/ 6 *e *Gamma(-1/3)*lowergamma|-----, -oo|
\ 3 / \ 3 /
- ----------------------------------------------------- + -------------------------------------------------
9*Gamma(2/3) 9*Gamma(2/3)
=
=
-2*pi*I -2*pi*I
------- / pi*I \ ------- / pi*I \
3 ___ 3 |e pi*I| 3 ___ 3 |e |
\/ 6 *e *Gamma(-1/3)*lowergamma|-----, 6*e | \/ 6 *e *Gamma(-1/3)*lowergamma|-----, -oo|
\ 3 / \ 3 /
- ----------------------------------------------------- + -------------------------------------------------
9*Gamma(2/3) 9*Gamma(2/3)
-2*pi*I -2*pi*I
------- / pi*I \ ------- / pi*I \
3 ___ 3 |e pi*I| 3 ___ 3 |e |
\/ 6 *e *Gamma(-1/3)*lowergamma|-----, 6*e | \/ 6 *e *Gamma(-1/3)*lowergamma|-----, -oo|
\ 3 / \ 3 /
- ----------------------------------------------------- + -------------------------------------------------
9*Gamma(2/3) 9*Gamma(2/3)
-6^(1/3)*exp(-2*pi*i/3)*gamma(-1/3)*lowergamma(exp_polar(pi*i)/3, 6*exp_polar(pi*i))/(9*gamma(2/3)) + 6^(1/3)*exp(-2*pi*i/3)*gamma(-1/3)*lowergamma(exp_polar(pi*i)/3, -oo)/(9*gamma(2/3))
Respuesta numérica
[src]
8.67110045710251e+2589063827999210513433879896283392779713211448514876998581
8.67110045710251e+2589063827999210513433879896283392779713211448514876998581
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.