Sr Examen
Integral de 13*x/(x^2+13*x+1) dx
Solución
Ha introducido
[src]
1 / | | 13*x | ------------- dx | 2 | x + 13*x + 1 | / 0
$$\int\limits_{0}^{1} \frac{13 x}{\left(x^{2} + 13 x\right) + 1}\, dx$$
Integral((13*x)/(x^2 + 13*x + 1), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / _____ \ \
|| _____ |2*\/ 165 *(13/2 + x)| |
||-\/ 165 *acoth|--------------------| |
/ || \ 165 / 2 |
| ||------------------------------------- for (13/2 + x) > 165/4| / 2 \
| 13*x || 330 | 13*log\1 + x + 13*x/
| ------------- dx = C - 338*|< | + ---------------------
| 2 || / _____ \ | 2
| x + 13*x + 1 || _____ |2*\/ 165 *(13/2 + x)| |
| ||-\/ 165 *atanh|--------------------| |
/ || \ 165 / 2 |
||------------------------------------- for (13/2 + x) < 165/4|
\\ 330 /
$$\int \frac{13 x}{\left(x^{2} + 13 x\right) + 1}\, dx = C - 338 \left(\begin{cases} - \frac{\sqrt{165} \operatorname{acoth}{\left(\frac{2 \sqrt{165} \left(x + \frac{13}{2}\right)}{165} \right)}}{330} & \text{for}\: \left(x + \frac{13}{2}\right)^{2} > \frac{165}{4} \\- \frac{\sqrt{165} \operatorname{atanh}{\left(\frac{2 \sqrt{165} \left(x + \frac{13}{2}\right)}{165} \right)}}{330} & \text{for}\: \left(x + \frac{13}{2}\right)^{2} < \frac{165}{4} \end{cases}\right) + \frac{13 \log{\left(x^{2} + 13 x + 1 \right)}}{2}$$
Gráfica
Respuesta
[src]
/ _____\ / _____\ / _____\ / _____\ / _____\ / _____\ / _____\ / _____\
|1 13*\/ 165 | |13 \/ 165 | |1 13*\/ 165 | |13 \/ 165 | |1 13*\/ 165 | |15 \/ 165 | |1 13*\/ 165 | |15 \/ 165 |
- 13*|- - ----------|*log|-- - -------| - 13*|- + ----------|*log|-- + -------| + 13*|- - ----------|*log|-- - -------| + 13*|- + ----------|*log|-- + -------|
\2 330 / \2 2 / \2 330 / \2 2 / \2 330 / \2 2 / \2 330 / \2 2 /
$$- 13 \left(\frac{1}{2} + \frac{13 \sqrt{165}}{330}\right) \log{\left(\frac{\sqrt{165}}{2} + \frac{13}{2} \right)} - 13 \left(\frac{1}{2} - \frac{13 \sqrt{165}}{330}\right) \log{\left(\frac{13}{2} - \frac{\sqrt{165}}{2} \right)} + 13 \left(\frac{1}{2} - \frac{13 \sqrt{165}}{330}\right) \log{\left(\frac{15}{2} - \frac{\sqrt{165}}{2} \right)} + 13 \left(\frac{1}{2} + \frac{13 \sqrt{165}}{330}\right) \log{\left(\frac{\sqrt{165}}{2} + \frac{15}{2} \right)}$$
=
=
/ _____\ / _____\ / _____\ / _____\ / _____\ / _____\ / _____\ / _____\
|1 13*\/ 165 | |13 \/ 165 | |1 13*\/ 165 | |13 \/ 165 | |1 13*\/ 165 | |15 \/ 165 | |1 13*\/ 165 | |15 \/ 165 |
- 13*|- - ----------|*log|-- - -------| - 13*|- + ----------|*log|-- + -------| + 13*|- - ----------|*log|-- - -------| + 13*|- + ----------|*log|-- + -------|
\2 330 / \2 2 / \2 330 / \2 2 / \2 330 / \2 2 / \2 330 / \2 2 /
$$- 13 \left(\frac{1}{2} + \frac{13 \sqrt{165}}{330}\right) \log{\left(\frac{\sqrt{165}}{2} + \frac{13}{2} \right)} - 13 \left(\frac{1}{2} - \frac{13 \sqrt{165}}{330}\right) \log{\left(\frac{13}{2} - \frac{\sqrt{165}}{2} \right)} + 13 \left(\frac{1}{2} - \frac{13 \sqrt{165}}{330}\right) \log{\left(\frac{15}{2} - \frac{\sqrt{165}}{2} \right)} + 13 \left(\frac{1}{2} + \frac{13 \sqrt{165}}{330}\right) \log{\left(\frac{\sqrt{165}}{2} + \frac{15}{2} \right)}$$
-13*(1/2 - 13*sqrt(165)/330)*log(13/2 - sqrt(165)/2) - 13*(1/2 + 13*sqrt(165)/330)*log(13/2 + sqrt(165)/2) + 13*(1/2 - 13*sqrt(165)/330)*log(15/2 - sqrt(165)/2) + 13*(1/2 + 13*sqrt(165)/330)*log(15/2 + sqrt(165)/2)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.