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 ___ / 2/3 2 3 ___\ 3 ___ / 3 ___\ 3 *atan|- ----- + ---------| | 1 \/ 3 *log\3 + x - x*\/ 3 / \/ 3 *log\x + \/ 3 / \ 3 3 / | ------ dx = C - ------------------------------ + -------------------- + ------------------------------ | 3 18 9 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 ___ / 2/3 3 ___\ 3 ___ / 3 ___\ 3 *atan|- ----- + -------| 3 ___ / 2/3\ 5/6
\/ 3 *log\\/ 3 / \/ 3 *log\1 + 3 - \/ 3 / \/ 3 *log\1 + \/ 3 / \ 3 3 / \/ 3 *log\3 / pi*3
- ---------------- - --------------------------- + -------------------- + ---------------------------- + --------------- + -------
9 18 9 9 18 54
$$- \frac{\sqrt[3]{3} \log{\left(\sqrt[3]{3} \right)}}{9} - \frac{\sqrt[3]{3} \log{\left(- \sqrt[3]{3} + 1 + 3^{\frac{2}{3}} \right)}}{18} + \frac{\sqrt[3]{3} \log{\left(3^{\frac{2}{3}} \right)}}{18} + \frac{3^{\frac{5}{6}} \operatorname{atan}{\left(- \frac{\sqrt{3}}{3} + \frac{2 \sqrt[6]{3}}{3} \right)}}{9} + \frac{\sqrt[3]{3} \log{\left(1 + \sqrt[3]{3} \right)}}{9} + \frac{3^{\frac{5}{6}} \pi}{54}$$
=
=
/ ___ 6 ___\
5/6 | \/ 3 2*\/ 3 |
3 ___ /3 ___\ 3 ___ / 2/3 3 ___\ 3 ___ / 3 ___\ 3 *atan|- ----- + -------| 3 ___ / 2/3\ 5/6
\/ 3 *log\\/ 3 / \/ 3 *log\1 + 3 - \/ 3 / \/ 3 *log\1 + \/ 3 / \ 3 3 / \/ 3 *log\3 / pi*3
- ---------------- - --------------------------- + -------------------- + ---------------------------- + --------------- + -------
9 18 9 9 18 54
$$- \frac{\sqrt[3]{3} \log{\left(\sqrt[3]{3} \right)}}{9} - \frac{\sqrt[3]{3} \log{\left(- \sqrt[3]{3} + 1 + 3^{\frac{2}{3}} \right)}}{18} + \frac{\sqrt[3]{3} \log{\left(3^{\frac{2}{3}} \right)}}{18} + \frac{3^{\frac{5}{6}} \operatorname{atan}{\left(- \frac{\sqrt{3}}{3} + \frac{2 \sqrt[6]{3}}{3} \right)}}{9} + \frac{\sqrt[3]{3} \log{\left(1 + \sqrt[3]{3} \right)}}{9} + \frac{3^{\frac{5}{6}} \pi}{54}$$
-3^(1/3)*log(3^(1/3))/9 - 3^(1/3)*log(1 + 3^(2/3) - 3^(1/3))/18 + 3^(1/3)*log(1 + 3^(1/3))/9 + 3^(5/6)*atan(-sqrt(3)/3 + 2*3^(1/6)/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.