Sr Examen
Integral de 1/(z^3-5z^2-7z-3) dz
Solución
Ha introducido
[src]
0 / | | 1 | ------------------- dz | 3 2 | z - 5*z - 7*z - 3 | / 3
$$\int\limits_{3}^{0} \frac{1}{\left(- 7 z + \left(z^{3} - 5 z^{2}\right)\right) - 3}\, dz$$
Integral(1/(z^3 - 5*z^2 - 7*z - 3), (z, 3, 0))
Respuesta (Indefinida)
[src]
/ 2 \
| / ____________________ \ |
| | / _____ | |
| | / 1 323*\/ 777 23 | |
| 47656*|3 / ---- + ----------- - ------------------------------| |
| |\/ 2072 4829832 ____________________| ____________________ |
| | / _____ | / _____ |
/ / ____________________ \ | | / 1 323*\/ 777 | / 1 323*\/ 777 |
| | / _____ | | | 1554*3 / ---- + ----------- | 1554*3 / ---- + ----------- |
| 1 | / 1 323*\/ 777 23 | | 1949 \ \/ 2072 4829832 / \/ 2072 4829832 23 |
| ------------------- dz = C + |3 / ---- + ----------- - ------------------------------|*log|- ---- + z - ------------------------------------------------------------------- - ------------------------------ + -----------------------------|
| 3 2 |\/ 2072 4829832 ____________________| | 323 323 323 ____________________|
| z - 5*z - 7*z - 3 | / _____ | | / _____ |
| | / 1 323*\/ 777 | | / 1 323*\/ 777 |
/ | 1554*3 / ---- + ----------- | | 323*3 / ---- + ----------- |
\ \/ 2072 4829832 / \ \/ 2072 4829832 /
$$\int \frac{1}{\left(- 7 z + \left(z^{3} - 5 z^{2}\right)\right) - 3}\, dz = C + \left(- \frac{23}{1554 \sqrt[3]{\frac{1}{2072} + \frac{323 \sqrt{777}}{4829832}}} + \sqrt[3]{\frac{1}{2072} + \frac{323 \sqrt{777}}{4829832}}\right) \log{\left(z - \frac{1949}{323} - \frac{1554 \sqrt[3]{\frac{1}{2072} + \frac{323 \sqrt{777}}{4829832}}}{323} - \frac{47656 \left(- \frac{23}{1554 \sqrt[3]{\frac{1}{2072} + \frac{323 \sqrt{777}}{4829832}}} + \sqrt[3]{\frac{1}{2072} + \frac{323 \sqrt{777}}{4829832}}\right)^{2}}{323} + \frac{23}{323 \sqrt[3]{\frac{1}{2072} + \frac{323 \sqrt{777}}{4829832}}} \right)}$$
Gráfica
Respuesta
[src]
/ / 2\\ / / 2\\
| | / ____________________ \ || | | / ____________________ \ ||
| | | / _____ | || | | | / _____ | ||
| | | / 1 323*\/ 777 23 | || | | | / 1 323*\/ 777 23 | ||
| | 47656*|3 / ---- + ----------- - ------------------------------| || | | 47656*|3 / ---- + ----------- - ------------------------------| ||
| | ____________________ |\/ 2072 4829832 ____________________| || | | ____________________ |\/ 2072 4829832 ____________________| ||
| | / _____ | / _____ | || | | / _____ | / _____ | ||
/ ____________________ \ | | / 1 323*\/ 777 | / 1 323*\/ 777 | || / ____________________ \ | | / 1 323*\/ 777 | / 1 323*\/ 777 | ||
| / _____ | | | 1554*3 / ---- + ----------- | 1554*3 / ---- + ----------- | || | / _____ | | | 1554*3 / ---- + ----------- | 1554*3 / ---- + ----------- | ||
| / 1 323*\/ 777 23 | | |1949 23 \/ 2072 4829832 \ \/ 2072 4829832 / || | / 1 323*\/ 777 23 | | |980 23 \/ 2072 4829832 \ \/ 2072 4829832 / ||
|3 / ---- + ----------- - ------------------------------|*|pi*I + log|---- - ----------------------------- + ------------------------------ + -------------------------------------------------------------------|| - |3 / ---- + ----------- - ------------------------------|*|pi*I + log|--- - ----------------------------- + ------------------------------ + -------------------------------------------------------------------||
|\/ 2072 4829832 ____________________| | |323 ____________________ 323 323 || |\/ 2072 4829832 ____________________| | |323 ____________________ 323 323 ||
| / _____ | | | / _____ || | / _____ | | | / _____ ||
| / 1 323*\/ 777 | | | / 1 323*\/ 777 || | / 1 323*\/ 777 | | | / 1 323*\/ 777 ||
| 1554*3 / ---- + ----------- | | | 323*3 / ---- + ----------- || | 1554*3 / ---- + ----------- | | | 323*3 / ---- + ----------- ||
\ \/ 2072 4829832 / \ \ \/ 2072 4829832 // \ \/ 2072 4829832 / \ \ \/ 2072 4829832 //
$$- \left(- \frac{23}{1554 \sqrt[3]{\frac{1}{2072} + \frac{323 \sqrt{777}}{4829832}}} + \sqrt[3]{\frac{1}{2072} + \frac{323 \sqrt{777}}{4829832}}\right) \left(\log{\left(- \frac{23}{323 \sqrt[3]{\frac{1}{2072} + \frac{323 \sqrt{777}}{4829832}}} + \frac{47656 \left(- \frac{23}{1554 \sqrt[3]{\frac{1}{2072} + \frac{323 \sqrt{777}}{4829832}}} + \sqrt[3]{\frac{1}{2072} + \frac{323 \sqrt{777}}{4829832}}\right)^{2}}{323} + \frac{1554 \sqrt[3]{\frac{1}{2072} + \frac{323 \sqrt{777}}{4829832}}}{323} + \frac{980}{323} \right)} + i \pi\right) + \left(- \frac{23}{1554 \sqrt[3]{\frac{1}{2072} + \frac{323 \sqrt{777}}{4829832}}} + \sqrt[3]{\frac{1}{2072} + \frac{323 \sqrt{777}}{4829832}}\right) \left(\log{\left(- \frac{23}{323 \sqrt[3]{\frac{1}{2072} + \frac{323 \sqrt{777}}{4829832}}} + \frac{47656 \left(- \frac{23}{1554 \sqrt[3]{\frac{1}{2072} + \frac{323 \sqrt{777}}{4829832}}} + \sqrt[3]{\frac{1}{2072} + \frac{323 \sqrt{777}}{4829832}}\right)^{2}}{323} + \frac{1554 \sqrt[3]{\frac{1}{2072} + \frac{323 \sqrt{777}}{4829832}}}{323} + \frac{1949}{323} \right)} + i \pi\right)$$
=
=
/ / 2\\ / / 2\\
| | / ____________________ \ || | | / ____________________ \ ||
| | | / _____ | || | | | / _____ | ||
| | | / 1 323*\/ 777 23 | || | | | / 1 323*\/ 777 23 | ||
| | 47656*|3 / ---- + ----------- - ------------------------------| || | | 47656*|3 / ---- + ----------- - ------------------------------| ||
| | ____________________ |\/ 2072 4829832 ____________________| || | | ____________________ |\/ 2072 4829832 ____________________| ||
| | / _____ | / _____ | || | | / _____ | / _____ | ||
/ ____________________ \ | | / 1 323*\/ 777 | / 1 323*\/ 777 | || / ____________________ \ | | / 1 323*\/ 777 | / 1 323*\/ 777 | ||
| / _____ | | | 1554*3 / ---- + ----------- | 1554*3 / ---- + ----------- | || | / _____ | | | 1554*3 / ---- + ----------- | 1554*3 / ---- + ----------- | ||
| / 1 323*\/ 777 23 | | |1949 23 \/ 2072 4829832 \ \/ 2072 4829832 / || | / 1 323*\/ 777 23 | | |980 23 \/ 2072 4829832 \ \/ 2072 4829832 / ||
|3 / ---- + ----------- - ------------------------------|*|pi*I + log|---- - ----------------------------- + ------------------------------ + -------------------------------------------------------------------|| - |3 / ---- + ----------- - ------------------------------|*|pi*I + log|--- - ----------------------------- + ------------------------------ + -------------------------------------------------------------------||
|\/ 2072 4829832 ____________________| | |323 ____________________ 323 323 || |\/ 2072 4829832 ____________________| | |323 ____________________ 323 323 ||
| / _____ | | | / _____ || | / _____ | | | / _____ ||
| / 1 323*\/ 777 | | | / 1 323*\/ 777 || | / 1 323*\/ 777 | | | / 1 323*\/ 777 ||
| 1554*3 / ---- + ----------- | | | 323*3 / ---- + ----------- || | 1554*3 / ---- + ----------- | | | 323*3 / ---- + ----------- ||
\ \/ 2072 4829832 / \ \ \/ 2072 4829832 // \ \/ 2072 4829832 / \ \ \/ 2072 4829832 //
$$- \left(- \frac{23}{1554 \sqrt[3]{\frac{1}{2072} + \frac{323 \sqrt{777}}{4829832}}} + \sqrt[3]{\frac{1}{2072} + \frac{323 \sqrt{777}}{4829832}}\right) \left(\log{\left(- \frac{23}{323 \sqrt[3]{\frac{1}{2072} + \frac{323 \sqrt{777}}{4829832}}} + \frac{47656 \left(- \frac{23}{1554 \sqrt[3]{\frac{1}{2072} + \frac{323 \sqrt{777}}{4829832}}} + \sqrt[3]{\frac{1}{2072} + \frac{323 \sqrt{777}}{4829832}}\right)^{2}}{323} + \frac{1554 \sqrt[3]{\frac{1}{2072} + \frac{323 \sqrt{777}}{4829832}}}{323} + \frac{980}{323} \right)} + i \pi\right) + \left(- \frac{23}{1554 \sqrt[3]{\frac{1}{2072} + \frac{323 \sqrt{777}}{4829832}}} + \sqrt[3]{\frac{1}{2072} + \frac{323 \sqrt{777}}{4829832}}\right) \left(\log{\left(- \frac{23}{323 \sqrt[3]{\frac{1}{2072} + \frac{323 \sqrt{777}}{4829832}}} + \frac{47656 \left(- \frac{23}{1554 \sqrt[3]{\frac{1}{2072} + \frac{323 \sqrt{777}}{4829832}}} + \sqrt[3]{\frac{1}{2072} + \frac{323 \sqrt{777}}{4829832}}\right)^{2}}{323} + \frac{1554 \sqrt[3]{\frac{1}{2072} + \frac{323 \sqrt{777}}{4829832}}}{323} + \frac{1949}{323} \right)} + i \pi\right)$$
((1/2072 + 323*sqrt(777)/4829832)^(1/3) - 23/(1554*(1/2072 + 323*sqrt(777)/4829832)^(1/3)))*(pi*i + log(1949/323 - 23/(323*(1/2072 + 323*sqrt(777)/4829832)^(1/3)) + 1554*(1/2072 + 323*sqrt(777)/4829832)^(1/3)/323 + 47656*((1/2072 + 323*sqrt(777)/4829832)^(1/3) - 23/(1554*(1/2072 + 323*sqrt(777)/4829832)^(1/3)))^2/323)) - ((1/2072 + 323*sqrt(777)/4829832)^(1/3) - 23/(1554*(1/2072 + 323*sqrt(777)/4829832)^(1/3)))*(pi*i + log(980/323 - 23/(323*(1/2072 + 323*sqrt(777)/4829832)^(1/3)) + 1554*(1/2072 + 323*sqrt(777)/4829832)^(1/3)/323 + 47656*((1/2072 + 323*sqrt(777)/4829832)^(1/3) - 23/(1554*(1/2072 + 323*sqrt(777)/4829832)^(1/3)))^2/323))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.