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