Sr Examen
Integral de 1/(x^3-3) dx
Solución
Ha introducido
[src]
1 / | | 1 | ------ dx | 3 | x - 3 | / 0
$$\int\limits_{0}^{1} \frac{1}{x^{3} - 3}\, dx$$
Integral(1/(x^3 - 3), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ ___ 6 ___\ / 5/6 |\/ 3 2*x*\/ 3 | | 3 *atan|----- + ---------| 3 ___ / 2/3 2 3 ___\ 3 ___ / 3 ___\ | 1 \ 3 3 / \/ 3 *log\3 + x + x*\/ 3 / \/ 3 *log\x - \/ 3 / | ------ dx = C - ---------------------------- - ------------------------------ + -------------------- | 3 9 18 9 | x - 3 | /
$$\int \frac{1}{x^{3} - 3}\, dx = C + \frac{\sqrt[3]{3} \log{\left(x - \sqrt[3]{3} \right)}}{9} - \frac{\sqrt[3]{3} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{18} - \frac{3^{\frac{5}{6}} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{9}$$
Gráfica
Respuesta
[src]
/ ___ 6 ___\
5/6 |\/ 3 2*\/ 3 |
3 ___ / /3 ___\\ 3 *atan|----- + -------| 3 ___ / 3 ___ 2/3\ 3 ___ / / 3 ___\\ 3 ___ / 2/3\ 5/6
\/ 3 *\pi*I + log\\/ 3 // \ 3 3 / \/ 3 *log\1 + \/ 3 + 3 / \/ 3 *\pi*I + log\-1 + \/ 3 // \/ 3 *log\3 / pi*3
- ------------------------- - -------------------------- - --------------------------- + ------------------------------ + --------------- + -------
9 9 18 9 18 54
$$- \frac{3^{\frac{5}{6}} \operatorname{atan}{\left(\frac{\sqrt{3}}{3} + \frac{2 \sqrt[6]{3}}{3} \right)}}{9} - \frac{\sqrt[3]{3} \log{\left(1 + \sqrt[3]{3} + 3^{\frac{2}{3}} \right)}}{18} + \frac{\sqrt[3]{3} \log{\left(3^{\frac{2}{3}} \right)}}{18} + \frac{3^{\frac{5}{6}} \pi}{54} - \frac{\sqrt[3]{3} \left(\log{\left(\sqrt[3]{3} \right)} + i \pi\right)}{9} + \frac{\sqrt[3]{3} \left(\log{\left(-1 + \sqrt[3]{3} \right)} + i \pi\right)}{9}$$
=
=
/ ___ 6 ___\
5/6 |\/ 3 2*\/ 3 |
3 ___ / /3 ___\\ 3 *atan|----- + -------| 3 ___ / 3 ___ 2/3\ 3 ___ / / 3 ___\\ 3 ___ / 2/3\ 5/6
\/ 3 *\pi*I + log\\/ 3 // \ 3 3 / \/ 3 *log\1 + \/ 3 + 3 / \/ 3 *\pi*I + log\-1 + \/ 3 // \/ 3 *log\3 / pi*3
- ------------------------- - -------------------------- - --------------------------- + ------------------------------ + --------------- + -------
9 9 18 9 18 54
$$- \frac{3^{\frac{5}{6}} \operatorname{atan}{\left(\frac{\sqrt{3}}{3} + \frac{2 \sqrt[6]{3}}{3} \right)}}{9} - \frac{\sqrt[3]{3} \log{\left(1 + \sqrt[3]{3} + 3^{\frac{2}{3}} \right)}}{18} + \frac{\sqrt[3]{3} \log{\left(3^{\frac{2}{3}} \right)}}{18} + \frac{3^{\frac{5}{6}} \pi}{54} - \frac{\sqrt[3]{3} \left(\log{\left(\sqrt[3]{3} \right)} + i \pi\right)}{9} + \frac{\sqrt[3]{3} \left(\log{\left(-1 + \sqrt[3]{3} \right)} + i \pi\right)}{9}$$
-3^(1/3)*(pi*i + log(3^(1/3)))/9 - 3^(5/6)*atan(sqrt(3)/3 + 2*3^(1/6)/3)/9 - 3^(1/3)*log(1 + 3^(1/3) + 3^(2/3))/18 + 3^(1/3)*(pi*i + log(-1 + 3^(1/3)))/9 + 3^(1/3)*log(3^(2/3))/18 + pi*3^(5/6)/54
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.