Sr Examen
Integral de x^2/(x^3+3*x+1)^3 dx
Solución
Ha introducido
[src]
1 / | | 2 | x | --------------- dx | 3 | / 3 \ | \x + 3*x + 1/ | / 0
$$\int\limits_{0}^{1} \frac{x^{2}}{\left(\left(x^{3} + 3 x\right) + 1\right)^{3}}\, dx$$
Integral(x^2/(x^3 + 3*x + 1)^3, (x, 0, 1))
Respuesta (Indefinida)
[src]
/ 2 \
| / _________________________ \ |
| | / ___ | |
| | / 131 7379*\/ 5 59 | |
| 29615625*|3 / --------- + ----------- - --------------------------------------| |
| |\/ 123018750 15377343750 _________________________| _________________________|
/ | | / ___ | / ___ |
| / _________________________ \ | | / 131 7379*\/ 5 | / 131 7379*\/ 5 |
| 2 4 5 2 3 | / ___ | | | 2278125*3 / --------- + ----------- | 681750*3 / --------- + ----------- |
| x 21 + 11*x + 18*x + 81*x + 90*x + 104*x | / 131 7379*\/ 5 59 | | 1534 \ \/ 123018750 15377343750 / 11918 \/ 123018750 15377343750 |
| --------------- dx = C + -------------------------------------------------- + |3 / --------- + ----------- - --------------------------------------|*log|- ---- + x - ----------------------------------------------------------------------------------- - -------------------------------------- + -------------------------------------|
| 3 6 3 4 2 |\/ 123018750 15377343750 _________________________| | 7379 7379 _________________________ 7379 |
| / 3 \ 450 + 450*x + 900*x + 2700*x + 2700*x + 4050*x | / ___ | | / ___ |
| \x + 3*x + 1/ | / 131 7379*\/ 5 | | / 131 7379*\/ 5 |
| | 2278125*3 / --------- + ----------- | | 4980825*3 / --------- + ----------- |
/ \ \/ 123018750 15377343750 / \ \/ 123018750 15377343750 /
$$\int \frac{x^{2}}{\left(\left(x^{3} + 3 x\right) + 1\right)^{3}}\, dx = C + \frac{18 x^{5} + 11 x^{4} + 90 x^{3} + 81 x^{2} + 104 x + 21}{450 x^{6} + 2700 x^{4} + 900 x^{3} + 4050 x^{2} + 2700 x + 450} + \left(- \frac{59}{2278125 \sqrt[3]{\frac{131}{123018750} + \frac{7379 \sqrt{5}}{15377343750}}} + \sqrt[3]{\frac{131}{123018750} + \frac{7379 \sqrt{5}}{15377343750}}\right) \log{\left(x - \frac{29615625 \left(- \frac{59}{2278125 \sqrt[3]{\frac{131}{123018750} + \frac{7379 \sqrt{5}}{15377343750}}} + \sqrt[3]{\frac{131}{123018750} + \frac{7379 \sqrt{5}}{15377343750}}\right)^{2}}{7379} - \frac{1534}{7379} - \frac{11918}{4980825 \sqrt[3]{\frac{131}{123018750} + \frac{7379 \sqrt{5}}{15377343750}}} + \frac{681750 \sqrt[3]{\frac{131}{123018750} + \frac{7379 \sqrt{5}}{15377343750}}}{7379} \right)}$$
Gráfica
Respuesta
[src]
/ 2 \ / 2 \
| / _________________________ \ | | / _________________________ \ |
| | / ___ | | | | / ___ | |
| | / 131 7379*\/ 5 59 | | | | / 131 7379*\/ 5 59 | |
| 29615625*|3 / --------- + ----------- - --------------------------------------| | | 29615625*|3 / --------- + ----------- - --------------------------------------| |
| |\/ 123018750 15377343750 _________________________| _________________________| | |\/ 123018750 15377343750 _________________________| _________________________|
| | / ___ | / ___ | | | / ___ | / ___ |
/ _________________________ \ | | / 131 7379*\/ 5 | / 131 7379*\/ 5 | / _________________________ \ | | / 131 7379*\/ 5 | / 131 7379*\/ 5 |
| / ___ | | | 2278125*3 / --------- + ----------- | 681750*3 / --------- + ----------- | | / ___ | | | 2278125*3 / --------- + ----------- | 681750*3 / --------- + ----------- |
4 | / 131 7379*\/ 5 59 | |5845 \ \/ 123018750 15377343750 / 11918 \/ 123018750 15377343750 | | / 131 7379*\/ 5 59 | | 1534 \ \/ 123018750 15377343750 / 11918 \/ 123018750 15377343750 |
- --- + |3 / --------- + ----------- - --------------------------------------|*log|---- - ----------------------------------------------------------------------------------- - -------------------------------------- + -------------------------------------| - |3 / --------- + ----------- - --------------------------------------|*log|- ---- - ----------------------------------------------------------------------------------- - -------------------------------------- + -------------------------------------|
225 |\/ 123018750 15377343750 _________________________| |7379 7379 _________________________ 7379 | |\/ 123018750 15377343750 _________________________| | 7379 7379 _________________________ 7379 |
| / ___ | | / ___ | | / ___ | | / ___ |
| / 131 7379*\/ 5 | | / 131 7379*\/ 5 | | / 131 7379*\/ 5 | | / 131 7379*\/ 5 |
| 2278125*3 / --------- + ----------- | | 4980825*3 / --------- + ----------- | | 2278125*3 / --------- + ----------- | | 4980825*3 / --------- + ----------- |
\ \/ 123018750 15377343750 / \ \/ 123018750 15377343750 / \ \/ 123018750 15377343750 / \ \/ 123018750 15377343750 /
$$- \frac{4}{225} + \left(- \frac{59}{2278125 \sqrt[3]{\frac{131}{123018750} + \frac{7379 \sqrt{5}}{15377343750}}} + \sqrt[3]{\frac{131}{123018750} + \frac{7379 \sqrt{5}}{15377343750}}\right) \log{\left(- \frac{29615625 \left(- \frac{59}{2278125 \sqrt[3]{\frac{131}{123018750} + \frac{7379 \sqrt{5}}{15377343750}}} + \sqrt[3]{\frac{131}{123018750} + \frac{7379 \sqrt{5}}{15377343750}}\right)^{2}}{7379} - \frac{11918}{4980825 \sqrt[3]{\frac{131}{123018750} + \frac{7379 \sqrt{5}}{15377343750}}} + \frac{5845}{7379} + \frac{681750 \sqrt[3]{\frac{131}{123018750} + \frac{7379 \sqrt{5}}{15377343750}}}{7379} \right)} - \left(- \frac{59}{2278125 \sqrt[3]{\frac{131}{123018750} + \frac{7379 \sqrt{5}}{15377343750}}} + \sqrt[3]{\frac{131}{123018750} + \frac{7379 \sqrt{5}}{15377343750}}\right) \log{\left(- \frac{29615625 \left(- \frac{59}{2278125 \sqrt[3]{\frac{131}{123018750} + \frac{7379 \sqrt{5}}{15377343750}}} + \sqrt[3]{\frac{131}{123018750} + \frac{7379 \sqrt{5}}{15377343750}}\right)^{2}}{7379} - \frac{1534}{7379} - \frac{11918}{4980825 \sqrt[3]{\frac{131}{123018750} + \frac{7379 \sqrt{5}}{15377343750}}} + \frac{681750 \sqrt[3]{\frac{131}{123018750} + \frac{7379 \sqrt{5}}{15377343750}}}{7379} \right)}$$
=
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/ 2 \ / 2 \
| / _________________________ \ | | / _________________________ \ |
| | / ___ | | | | / ___ | |
| | / 131 7379*\/ 5 59 | | | | / 131 7379*\/ 5 59 | |
| 29615625*|3 / --------- + ----------- - --------------------------------------| | | 29615625*|3 / --------- + ----------- - --------------------------------------| |
| |\/ 123018750 15377343750 _________________________| _________________________| | |\/ 123018750 15377343750 _________________________| _________________________|
| | / ___ | / ___ | | | / ___ | / ___ |
/ _________________________ \ | | / 131 7379*\/ 5 | / 131 7379*\/ 5 | / _________________________ \ | | / 131 7379*\/ 5 | / 131 7379*\/ 5 |
| / ___ | | | 2278125*3 / --------- + ----------- | 681750*3 / --------- + ----------- | | / ___ | | | 2278125*3 / --------- + ----------- | 681750*3 / --------- + ----------- |
4 | / 131 7379*\/ 5 59 | |5845 \ \/ 123018750 15377343750 / 11918 \/ 123018750 15377343750 | | / 131 7379*\/ 5 59 | | 1534 \ \/ 123018750 15377343750 / 11918 \/ 123018750 15377343750 |
- --- + |3 / --------- + ----------- - --------------------------------------|*log|---- - ----------------------------------------------------------------------------------- - -------------------------------------- + -------------------------------------| - |3 / --------- + ----------- - --------------------------------------|*log|- ---- - ----------------------------------------------------------------------------------- - -------------------------------------- + -------------------------------------|
225 |\/ 123018750 15377343750 _________________________| |7379 7379 _________________________ 7379 | |\/ 123018750 15377343750 _________________________| | 7379 7379 _________________________ 7379 |
| / ___ | | / ___ | | / ___ | | / ___ |
| / 131 7379*\/ 5 | | / 131 7379*\/ 5 | | / 131 7379*\/ 5 | | / 131 7379*\/ 5 |
| 2278125*3 / --------- + ----------- | | 4980825*3 / --------- + ----------- | | 2278125*3 / --------- + ----------- | | 4980825*3 / --------- + ----------- |
\ \/ 123018750 15377343750 / \ \/ 123018750 15377343750 / \ \/ 123018750 15377343750 / \ \/ 123018750 15377343750 /
$$- \frac{4}{225} + \left(- \frac{59}{2278125 \sqrt[3]{\frac{131}{123018750} + \frac{7379 \sqrt{5}}{15377343750}}} + \sqrt[3]{\frac{131}{123018750} + \frac{7379 \sqrt{5}}{15377343750}}\right) \log{\left(- \frac{29615625 \left(- \frac{59}{2278125 \sqrt[3]{\frac{131}{123018750} + \frac{7379 \sqrt{5}}{15377343750}}} + \sqrt[3]{\frac{131}{123018750} + \frac{7379 \sqrt{5}}{15377343750}}\right)^{2}}{7379} - \frac{11918}{4980825 \sqrt[3]{\frac{131}{123018750} + \frac{7379 \sqrt{5}}{15377343750}}} + \frac{5845}{7379} + \frac{681750 \sqrt[3]{\frac{131}{123018750} + \frac{7379 \sqrt{5}}{15377343750}}}{7379} \right)} - \left(- \frac{59}{2278125 \sqrt[3]{\frac{131}{123018750} + \frac{7379 \sqrt{5}}{15377343750}}} + \sqrt[3]{\frac{131}{123018750} + \frac{7379 \sqrt{5}}{15377343750}}\right) \log{\left(- \frac{29615625 \left(- \frac{59}{2278125 \sqrt[3]{\frac{131}{123018750} + \frac{7379 \sqrt{5}}{15377343750}}} + \sqrt[3]{\frac{131}{123018750} + \frac{7379 \sqrt{5}}{15377343750}}\right)^{2}}{7379} - \frac{1534}{7379} - \frac{11918}{4980825 \sqrt[3]{\frac{131}{123018750} + \frac{7379 \sqrt{5}}{15377343750}}} + \frac{681750 \sqrt[3]{\frac{131}{123018750} + \frac{7379 \sqrt{5}}{15377343750}}}{7379} \right)}$$
-4/225 + ((131/123018750 + 7379*sqrt(5)/15377343750)^(1/3) - 59/(2278125*(131/123018750 + 7379*sqrt(5)/15377343750)^(1/3)))*log(5845/7379 - 29615625*((131/123018750 + 7379*sqrt(5)/15377343750)^(1/3) - 59/(2278125*(131/123018750 + 7379*sqrt(5)/15377343750)^(1/3)))^2/7379 - 11918/(4980825*(131/123018750 + 7379*sqrt(5)/15377343750)^(1/3)) + 681750*(131/123018750 + 7379*sqrt(5)/15377343750)^(1/3)/7379) - ((131/123018750 + 7379*sqrt(5)/15377343750)^(1/3) - 59/(2278125*(131/123018750 + 7379*sqrt(5)/15377343750)^(1/3)))*log(-1534/7379 - 29615625*((131/123018750 + 7379*sqrt(5)/15377343750)^(1/3) - 59/(2278125*(131/123018750 + 7379*sqrt(5)/15377343750)^(1/3)))^2/7379 - 11918/(4980825*(131/123018750 + 7379*sqrt(5)/15377343750)^(1/3)) + 681750*(131/123018750 + 7379*sqrt(5)/15377343750)^(1/3)/7379)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.