Sr Examen
Integral de x/(x^3-8) dx
Solución
Ha introducido
[src]
1 / | | x | ------ dx | 3 | x - 8 | / 0
$$\int\limits_{0}^{1} \frac{x}{x^{3} - 8}\, dx$$
Integral(x/(x^3 - 8), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ ___ \ / ___ |\/ 3 *(1 + x)| | / 2 \ \/ 3 *atan|-------------| | x log\4 + x + 2*x/ log(-2 + x) \ 3 / | ------ dx = C - ----------------- + ----------- + ------------------------- | 3 12 6 6 | x - 8 | /
$$\int \frac{x}{x^{3} - 8}\, dx = C + \frac{\log{\left(x - 2 \right)}}{6} - \frac{\log{\left(x^{2} + 2 x + 4 \right)}}{12} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(x + 1\right)}{3} \right)}}{6}$$
Gráfica
Respuesta
[src]
/ ___\
___ |2*\/ 3 |
___ \/ 3 *atan|-------|
log(2) log(7) log(4) pi*\/ 3 \ 3 /
- ------ - ------ + ------ - -------- + -------------------
6 12 12 36 6
$$- \frac{\log{\left(7 \right)}}{12} - \frac{\sqrt{3} \pi}{36} - \frac{\log{\left(2 \right)}}{6} + \frac{\log{\left(4 \right)}}{12} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3}}{3} \right)}}{6}$$
=
=
/ ___\
___ |2*\/ 3 |
___ \/ 3 *atan|-------|
log(2) log(7) log(4) pi*\/ 3 \ 3 /
- ------ - ------ + ------ - -------- + -------------------
6 12 12 36 6
$$- \frac{\log{\left(7 \right)}}{12} - \frac{\sqrt{3} \pi}{36} - \frac{\log{\left(2 \right)}}{6} + \frac{\log{\left(4 \right)}}{12} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3}}{3} \right)}}{6}$$
-log(2)/6 - log(7)/12 + log(4)/12 - pi*sqrt(3)/36 + sqrt(3)*atan(2*sqrt(3)/3)/6
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.