Sr Examen
Integral de (x^3-8)^-1 dx
Solución
Ha introducido
[src]
1 / | | 1 | ------ dx | 3 | x - 8 | / 0
$$\int\limits_{0}^{1} \frac{1}{x^{3} - 8}\, dx$$
Integral(1/(x^3 - 8), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ ___ \ / ___ |\/ 3 *(1 + x)| | / 2 \ \/ 3 *atan|-------------| | 1 log\4 + x + 2*x/ log(-2 + x) \ 3 / | ------ dx = C - ----------------- + ----------- - ------------------------- | 3 24 12 12 | x - 8 | /
$$\int \frac{1}{x^{3} - 8}\, dx = C + \frac{\log{\left(x - 2 \right)}}{12} - \frac{\log{\left(x^{2} + 2 x + 4 \right)}}{24} - \frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(x + 1\right)}{3} \right)}}{12}$$
Gráfica
Respuesta
[src]
/ ___\
___ |2*\/ 3 |
\/ 3 *atan|-------| ___
log(2) log(7) log(4) \ 3 / pi*\/ 3
- ------ - ------ + ------ - ------------------- + --------
12 24 24 12 72
$$- \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3}}{3} \right)}}{12} - \frac{\log{\left(7 \right)}}{24} - \frac{\log{\left(2 \right)}}{12} + \frac{\log{\left(4 \right)}}{24} + \frac{\sqrt{3} \pi}{72}$$
=
=
/ ___\
___ |2*\/ 3 |
\/ 3 *atan|-------| ___
log(2) log(7) log(4) \ 3 / pi*\/ 3
- ------ - ------ + ------ - ------------------- + --------
12 24 24 12 72
$$- \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3}}{3} \right)}}{12} - \frac{\log{\left(7 \right)}}{24} - \frac{\log{\left(2 \right)}}{12} + \frac{\log{\left(4 \right)}}{24} + \frac{\sqrt{3} \pi}{72}$$
-log(2)/12 - log(7)/24 + log(4)/24 - sqrt(3)*atan(2*sqrt(3)/3)/12 + pi*sqrt(3)/72
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.