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