Sr Examen
Integral de (6x+22)/(x^3+12x^2+47x+6) dx
Solución
Ha introducido
[src]
1 / | | 6*x + 22 | --------------------- dx | 3 2 | x + 12*x + 47*x + 6 | / 0
$$\int\limits_{0}^{1} \frac{6 x + 22}{\left(47 x + \left(x^{3} + 12 x^{2}\right)\right) + 6}\, dx$$
Integral((6*x + 22)/(x^3 + 12*x^2 + 47*x + 6), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ 2 \
| / __________________________ \ |
| | / _______ | | / 2 \
| | / 81 267243*\/ 59046 | | | / _______________________ \ |
| | 3 / ----- + ---------------- | | | | / _______ | |
| | \/ 78728 3099048992 1993 | | | | / 1 81*\/ 59046 1 | |
| 20075640*|- ------------------------------- + -------------------------------------| | | 78728*|3 / ------ + ------------ - ----------------------------------| |
/ __________________________ \ | | 3 __________________________| __________________________ | | |\/ 157456 3099048992 _______________________| _______________________ |
| / _______ | | | / _______ | / _______ | | | / _______ | / _______ |
/ | / 81 267243*\/ 59046 | | | / 81 267243*\/ 59046 | / 81 267243*\/ 59046 | / _______________________ \ | | / 1 81*\/ 59046 | / 1 81*\/ 59046 |
| | 3 / ----- + ---------------- | | | 78728*3 / ----- + ---------------- | 1850108*3 / ----- + ---------------- | | / _______ | | | 78728*3 / ------ + ------------ | 39364*3 / ------ + ------------ |
| 6*x + 22 | \/ 78728 3099048992 1993 | |17514 \ \/ 78728 3099048992 / \/ 78728 3099048992 93671 | | / 1 81*\/ 59046 1 | |970 \ \/ 157456 3099048992 / \/ 157456 3099048992 1 |
| --------------------- dx = C + 6*|- ------------------------------- + -------------------------------------|*log|----- + x - ------------------------------------------------------------------------------------- - --------------------------------------- + --------------------------------------| + 22*|3 / ------ + ------------ - ----------------------------------|*log|--- + x - -------------------------------------------------------------------------- - ---------------------------------- + --------------------------------|
| 3 2 | 3 __________________________| |89081 89081 267243 __________________________| |\/ 157456 3099048992 _______________________| |243 243 243 _______________________|
| x + 12*x + 47*x + 6 | / _______ | | / _______ | | / _______ | | / _______ |
| | / 81 267243*\/ 59046 | | / 81 267243*\/ 59046 | | / 1 81*\/ 59046 | | / 1 81*\/ 59046 |
/ | 78728*3 / ----- + ---------------- | | 178162*3 / ----- + ---------------- | | 78728*3 / ------ + ------------ | | 486*3 / ------ + ------------ |
\ \/ 78728 3099048992 / \ \/ 78728 3099048992 / \ \/ 157456 3099048992 / \ \/ 157456 3099048992 /
$$\int \frac{6 x + 22}{\left(47 x + \left(x^{3} + 12 x^{2}\right)\right) + 6}\, dx = C + 22 \left(- \frac{1}{78728 \sqrt[3]{\frac{1}{157456} + \frac{81 \sqrt{59046}}{3099048992}}} + \sqrt[3]{\frac{1}{157456} + \frac{81 \sqrt{59046}}{3099048992}}\right) \log{\left(x - \frac{39364 \sqrt[3]{\frac{1}{157456} + \frac{81 \sqrt{59046}}{3099048992}}}{243} - \frac{78728 \left(- \frac{1}{78728 \sqrt[3]{\frac{1}{157456} + \frac{81 \sqrt{59046}}{3099048992}}} + \sqrt[3]{\frac{1}{157456} + \frac{81 \sqrt{59046}}{3099048992}}\right)^{2}}{243} + \frac{1}{486 \sqrt[3]{\frac{1}{157456} + \frac{81 \sqrt{59046}}{3099048992}}} + \frac{970}{243} \right)} + 6 \left(- \frac{\sqrt[3]{\frac{81}{78728} + \frac{267243 \sqrt{59046}}{3099048992}}}{3} + \frac{1993}{78728 \sqrt[3]{\frac{81}{78728} + \frac{267243 \sqrt{59046}}{3099048992}}}\right) \log{\left(x - \frac{1850108 \sqrt[3]{\frac{81}{78728} + \frac{267243 \sqrt{59046}}{3099048992}}}{267243} - \frac{20075640 \left(- \frac{\sqrt[3]{\frac{81}{78728} + \frac{267243 \sqrt{59046}}{3099048992}}}{3} + \frac{1993}{78728 \sqrt[3]{\frac{81}{78728} + \frac{267243 \sqrt{59046}}{3099048992}}}\right)^{2}}{89081} + \frac{17514}{89081} + \frac{93671}{178162 \sqrt[3]{\frac{81}{78728} + \frac{267243 \sqrt{59046}}{3099048992}}} \right)}$$
Gráfica
Respuesta
[src]
/ 2 \ / 2 \
| / ________________________ \ | | / ________________________ \ |
| | / _______ | | | | / _______ | |
| | / 733 29727*\/ 59046 245 | | | | / 733 29727*\/ 59046 245 | |
| 1200602*|3 / ---- + --------------- - ----------------------------------| | | 1200602*|3 / ---- + --------------- - ----------------------------------| |
| |\/ 9841 96845281 ________________________| ________________________ | | |\/ 9841 96845281 ________________________| ________________________ |
| | / _______ | / _______ | | | / _______ | / _______ |
/ ________________________ \ | | / 733 29727*\/ 59046 | / 733 29727*\/ 59046 | / ________________________ \ | | / 733 29727*\/ 59046 | / 733 29727*\/ 59046 |
| / _______ | | | 9841*3 / ---- + --------------- | 9841*3 / ---- + --------------- | | / _______ | | | 9841*3 / ---- + --------------- | 9841*3 / ---- + --------------- |
| / 733 29727*\/ 59046 245 | |386125 \ \/ 9841 96845281 / \/ 9841 96845281 245 | | / 733 29727*\/ 59046 245 | |296944 \ \/ 9841 96845281 / \/ 9841 96845281 245 |
|3 / ---- + --------------- - ----------------------------------|*log|------ - ----------------------------------------------------------------------------- - ---------------------------------- + -----------------------------------| - |3 / ---- + --------------- - ----------------------------------|*log|------ - ----------------------------------------------------------------------------- - ---------------------------------- + -----------------------------------|
|\/ 9841 96845281 ________________________| |89181 89181 89181 ________________________| |\/ 9841 96845281 ________________________| |89181 89181 89181 ________________________|
| / _______ | | / _______ | | / _______ | | / _______ |
| / 733 29727*\/ 59046 | | / 733 29727*\/ 59046 | | / 733 29727*\/ 59046 | | / 733 29727*\/ 59046 |
| 9841*3 / ---- + --------------- | | 89181*3 / ---- + --------------- | | 9841*3 / ---- + --------------- | | 89181*3 / ---- + --------------- |
\ \/ 9841 96845281 / \ \/ 9841 96845281 / \ \/ 9841 96845281 / \ \/ 9841 96845281 /
$$\left(- \frac{245}{9841 \sqrt[3]{\frac{733}{9841} + \frac{29727 \sqrt{59046}}{96845281}}} + \sqrt[3]{\frac{733}{9841} + \frac{29727 \sqrt{59046}}{96845281}}\right) \log{\left(- \frac{1200602 \left(- \frac{245}{9841 \sqrt[3]{\frac{733}{9841} + \frac{29727 \sqrt{59046}}{96845281}}} + \sqrt[3]{\frac{733}{9841} + \frac{29727 \sqrt{59046}}{96845281}}\right)^{2}}{89181} - \frac{9841 \sqrt[3]{\frac{733}{9841} + \frac{29727 \sqrt{59046}}{96845281}}}{89181} + \frac{245}{89181 \sqrt[3]{\frac{733}{9841} + \frac{29727 \sqrt{59046}}{96845281}}} + \frac{386125}{89181} \right)} - \left(- \frac{245}{9841 \sqrt[3]{\frac{733}{9841} + \frac{29727 \sqrt{59046}}{96845281}}} + \sqrt[3]{\frac{733}{9841} + \frac{29727 \sqrt{59046}}{96845281}}\right) \log{\left(- \frac{1200602 \left(- \frac{245}{9841 \sqrt[3]{\frac{733}{9841} + \frac{29727 \sqrt{59046}}{96845281}}} + \sqrt[3]{\frac{733}{9841} + \frac{29727 \sqrt{59046}}{96845281}}\right)^{2}}{89181} - \frac{9841 \sqrt[3]{\frac{733}{9841} + \frac{29727 \sqrt{59046}}{96845281}}}{89181} + \frac{245}{89181 \sqrt[3]{\frac{733}{9841} + \frac{29727 \sqrt{59046}}{96845281}}} + \frac{296944}{89181} \right)}$$
=
=
/ 2 \ / 2 \
| / ________________________ \ | | / ________________________ \ |
| | / _______ | | | | / _______ | |
| | / 733 29727*\/ 59046 245 | | | | / 733 29727*\/ 59046 245 | |
| 1200602*|3 / ---- + --------------- - ----------------------------------| | | 1200602*|3 / ---- + --------------- - ----------------------------------| |
| |\/ 9841 96845281 ________________________| ________________________ | | |\/ 9841 96845281 ________________________| ________________________ |
| | / _______ | / _______ | | | / _______ | / _______ |
/ ________________________ \ | | / 733 29727*\/ 59046 | / 733 29727*\/ 59046 | / ________________________ \ | | / 733 29727*\/ 59046 | / 733 29727*\/ 59046 |
| / _______ | | | 9841*3 / ---- + --------------- | 9841*3 / ---- + --------------- | | / _______ | | | 9841*3 / ---- + --------------- | 9841*3 / ---- + --------------- |
| / 733 29727*\/ 59046 245 | |386125 \ \/ 9841 96845281 / \/ 9841 96845281 245 | | / 733 29727*\/ 59046 245 | |296944 \ \/ 9841 96845281 / \/ 9841 96845281 245 |
|3 / ---- + --------------- - ----------------------------------|*log|------ - ----------------------------------------------------------------------------- - ---------------------------------- + -----------------------------------| - |3 / ---- + --------------- - ----------------------------------|*log|------ - ----------------------------------------------------------------------------- - ---------------------------------- + -----------------------------------|
|\/ 9841 96845281 ________________________| |89181 89181 89181 ________________________| |\/ 9841 96845281 ________________________| |89181 89181 89181 ________________________|
| / _______ | | / _______ | | / _______ | | / _______ |
| / 733 29727*\/ 59046 | | / 733 29727*\/ 59046 | | / 733 29727*\/ 59046 | | / 733 29727*\/ 59046 |
| 9841*3 / ---- + --------------- | | 89181*3 / ---- + --------------- | | 9841*3 / ---- + --------------- | | 89181*3 / ---- + --------------- |
\ \/ 9841 96845281 / \ \/ 9841 96845281 / \ \/ 9841 96845281 / \ \/ 9841 96845281 /
$$\left(- \frac{245}{9841 \sqrt[3]{\frac{733}{9841} + \frac{29727 \sqrt{59046}}{96845281}}} + \sqrt[3]{\frac{733}{9841} + \frac{29727 \sqrt{59046}}{96845281}}\right) \log{\left(- \frac{1200602 \left(- \frac{245}{9841 \sqrt[3]{\frac{733}{9841} + \frac{29727 \sqrt{59046}}{96845281}}} + \sqrt[3]{\frac{733}{9841} + \frac{29727 \sqrt{59046}}{96845281}}\right)^{2}}{89181} - \frac{9841 \sqrt[3]{\frac{733}{9841} + \frac{29727 \sqrt{59046}}{96845281}}}{89181} + \frac{245}{89181 \sqrt[3]{\frac{733}{9841} + \frac{29727 \sqrt{59046}}{96845281}}} + \frac{386125}{89181} \right)} - \left(- \frac{245}{9841 \sqrt[3]{\frac{733}{9841} + \frac{29727 \sqrt{59046}}{96845281}}} + \sqrt[3]{\frac{733}{9841} + \frac{29727 \sqrt{59046}}{96845281}}\right) \log{\left(- \frac{1200602 \left(- \frac{245}{9841 \sqrt[3]{\frac{733}{9841} + \frac{29727 \sqrt{59046}}{96845281}}} + \sqrt[3]{\frac{733}{9841} + \frac{29727 \sqrt{59046}}{96845281}}\right)^{2}}{89181} - \frac{9841 \sqrt[3]{\frac{733}{9841} + \frac{29727 \sqrt{59046}}{96845281}}}{89181} + \frac{245}{89181 \sqrt[3]{\frac{733}{9841} + \frac{29727 \sqrt{59046}}{96845281}}} + \frac{296944}{89181} \right)}$$
((733/9841 + 29727*sqrt(59046)/96845281)^(1/3) - 245/(9841*(733/9841 + 29727*sqrt(59046)/96845281)^(1/3)))*log(386125/89181 - 1200602*((733/9841 + 29727*sqrt(59046)/96845281)^(1/3) - 245/(9841*(733/9841 + 29727*sqrt(59046)/96845281)^(1/3)))^2/89181 - 9841*(733/9841 + 29727*sqrt(59046)/96845281)^(1/3)/89181 + 245/(89181*(733/9841 + 29727*sqrt(59046)/96845281)^(1/3))) - ((733/9841 + 29727*sqrt(59046)/96845281)^(1/3) - 245/(9841*(733/9841 + 29727*sqrt(59046)/96845281)^(1/3)))*log(296944/89181 - 1200602*((733/9841 + 29727*sqrt(59046)/96845281)^(1/3) - 245/(9841*(733/9841 + 29727*sqrt(59046)/96845281)^(1/3)))^2/89181 - 9841*(733/9841 + 29727*sqrt(59046)/96845281)^(1/3)/89181 + 245/(89181*(733/9841 + 29727*sqrt(59046)/96845281)^(1/3)))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.