Sr Examen
Integral de 1/(x^3-9) dx
Solución
Ha introducido
[src]
1 / | | 1 | ------ dx | 3 | x - 9 | / 0
$$\int\limits_{0}^{1} \frac{1}{x^{3} - 9}\, dx$$
Integral(1/(x^3 - 9), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ ___ 5/6\ / 6 ___ |\/ 3 2*x*3 | | \/ 3 *atan|----- + --------| 2/3 / 2 3 ___ 2/3\ 2/3 / 2/3\ | 1 \ 3 9 / 3 *log\x + 3*\/ 3 + x*3 / 3 *log\x - 3 / | ------ dx = C - ---------------------------- - ------------------------------- + ------------------ | 3 9 54 27 | x - 9 | /
$$\int \frac{1}{x^{3} - 9}\, dx = C + \frac{3^{\frac{2}{3}} \log{\left(x - 3^{\frac{2}{3}} \right)}}{27} - \frac{3^{\frac{2}{3}} \log{\left(x^{2} + 3^{\frac{2}{3}} x + 3 \sqrt[3]{3} \right)}}{54} - \frac{\sqrt[6]{3} \operatorname{atan}{\left(\frac{2 \cdot 3^{\frac{5}{6}} x}{9} + \frac{\sqrt{3}}{3} \right)}}{9}$$
Gráfica
Respuesta
[src]
/ ___ 5/6\
6 ___ |\/ 3 2*3 |
\/ 3 *atan|----- + ------| 2/3 / / 2/3\\ 2/3 / 2/3 3 ___\ 2/3 / / 2/3\\ 6 ___ 2/3 / 3 ___\
\ 3 9 / 3 *\pi*I + log\3 // 3 *log\1 + 3 + 3*\/ 3 / 3 *\pi*I + log\-1 + 3 // pi*\/ 3 3 *log\3*\/ 3 /
- -------------------------- - ----------------------- - ---------------------------- + ---------------------------- + -------- + -----------------
9 27 54 27 54 54
$$- \frac{\sqrt[6]{3} \operatorname{atan}{\left(\frac{2 \cdot 3^{\frac{5}{6}}}{9} + \frac{\sqrt{3}}{3} \right)}}{9} - \frac{3^{\frac{2}{3}} \log{\left(1 + 3^{\frac{2}{3}} + 3 \sqrt[3]{3} \right)}}{54} + \frac{3^{\frac{2}{3}} \log{\left(3 \sqrt[3]{3} \right)}}{54} + \frac{\sqrt[6]{3} \pi}{54} - \frac{3^{\frac{2}{3}} \left(\log{\left(3^{\frac{2}{3}} \right)} + i \pi\right)}{27} + \frac{3^{\frac{2}{3}} \left(\log{\left(-1 + 3^{\frac{2}{3}} \right)} + i \pi\right)}{27}$$
=
=
/ ___ 5/6\
6 ___ |\/ 3 2*3 |
\/ 3 *atan|----- + ------| 2/3 / / 2/3\\ 2/3 / 2/3 3 ___\ 2/3 / / 2/3\\ 6 ___ 2/3 / 3 ___\
\ 3 9 / 3 *\pi*I + log\3 // 3 *log\1 + 3 + 3*\/ 3 / 3 *\pi*I + log\-1 + 3 // pi*\/ 3 3 *log\3*\/ 3 /
- -------------------------- - ----------------------- - ---------------------------- + ---------------------------- + -------- + -----------------
9 27 54 27 54 54
$$- \frac{\sqrt[6]{3} \operatorname{atan}{\left(\frac{2 \cdot 3^{\frac{5}{6}}}{9} + \frac{\sqrt{3}}{3} \right)}}{9} - \frac{3^{\frac{2}{3}} \log{\left(1 + 3^{\frac{2}{3}} + 3 \sqrt[3]{3} \right)}}{54} + \frac{3^{\frac{2}{3}} \log{\left(3 \sqrt[3]{3} \right)}}{54} + \frac{\sqrt[6]{3} \pi}{54} - \frac{3^{\frac{2}{3}} \left(\log{\left(3^{\frac{2}{3}} \right)} + i \pi\right)}{27} + \frac{3^{\frac{2}{3}} \left(\log{\left(-1 + 3^{\frac{2}{3}} \right)} + i \pi\right)}{27}$$
-3^(1/6)*atan(sqrt(3)/3 + 2*3^(5/6)/9)/9 - 3^(2/3)*(pi*i + log(3^(2/3)))/27 - 3^(2/3)*log(1 + 3^(2/3) + 3*3^(1/3))/54 + 3^(2/3)*(pi*i + log(-1 + 3^(2/3)))/27 + pi*3^(1/6)/54 + 3^(2/3)*log(3*3^(1/3))/54
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.