Sr Examen
Integral de 1/((x^2-5)*(x+6)) dx
Solución
Ha introducido
[src]
1 / | | 1 | ---------------- dx | / 2 \ | \x - 5/*(x + 6) | / 0
$$\int\limits_{0}^{1} \frac{1}{\left(x + 6\right) \left(x^{2} - 5\right)}\, dx$$
Integral(1/((x^2 - 5)*(x + 6)), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / ___\ \
|| ___ |x*\/ 5 | |
||-\/ 5 *acoth|-------| |
|| \ 5 / 2 |
||---------------------- for x > 5|
|| 5 |
6*|< |
|| / ___\ |
|| ___ |x*\/ 5 | |
||-\/ 5 *atanh|-------| |
/ || \ 5 / 2 |
| / 2\ ||---------------------- for x < 5|
| 1 log\-5 + x / log(6 + x) \\ 5 /
| ---------------- dx = C - ------------ + ---------- + ---------------------------------------
| / 2 \ 62 31 31
| \x - 5/*(x + 6)
|
/
$$\int \frac{1}{\left(x + 6\right) \left(x^{2} - 5\right)}\, dx = C + \frac{6 \left(\begin{cases} - \frac{\sqrt{5} \operatorname{acoth}{\left(\frac{\sqrt{5} x}{5} \right)}}{5} & \text{for}\: x^{2} > 5 \\- \frac{\sqrt{5} \operatorname{atanh}{\left(\frac{\sqrt{5} x}{5} \right)}}{5} & \text{for}\: x^{2} < 5 \end{cases}\right)}{31} + \frac{\log{\left(x + 6 \right)}}{31} - \frac{\log{\left(x^{2} - 5 \right)}}{62}$$
Gráfica
Respuesta
[src]
/ 2\ / / 2 \\ / 2\ / / 2 \\
| / ___\ | | | / ___\ || | / ___\ | | | / ___\ ||
| | 1 3*\/ 5 | | | | | 1 3*\/ 5 | || | | 1 3*\/ 5 | | | | | 1 3*\/ 5 | ||
/ ___\ | ___ 163370*|- -- - -------| | / ___\ | | 163370*|- -- + -------| ___|| / ___\ | ___ 163370*|- -- - -------| | / ___\ | | 163370*|- -- + -------| ___||
log(6) log(7) | 1 3*\/ 5 | | 679 31*\/ 5 \ 62 155 / | | 1 3*\/ 5 | | |679 \ 62 155 / 31*\/ 5 || | 1 3*\/ 5 | | 697 31*\/ 5 \ 62 155 / | | 1 3*\/ 5 | | |697 \ 62 155 / 31*\/ 5 ||
- ------ + ------ + |- -- - -------|*log|- --- - -------- + ------------------------| + |- -- + -------|*|pi*I + log|--- - ------------------------ - --------|| - |- -- - -------|*log|- --- - -------- + ------------------------| - |- -- + -------|*|pi*I + log|--- - ------------------------ - --------||
31 31 \ 62 155 / \ 18 3 9 / \ 62 155 / \ \ 18 9 3 // \ 62 155 / \ 18 3 9 / \ 62 155 / \ \ 18 9 3 //
$$\left(- \frac{3 \sqrt{5}}{155} - \frac{1}{62}\right) \log{\left(- \frac{679}{18} - \frac{31 \sqrt{5}}{3} + \frac{163370 \left(- \frac{3 \sqrt{5}}{155} - \frac{1}{62}\right)^{2}}{9} \right)} - \frac{\log{\left(6 \right)}}{31} - \left(- \frac{3 \sqrt{5}}{155} - \frac{1}{62}\right) \log{\left(- \frac{697}{18} - \frac{31 \sqrt{5}}{3} + \frac{163370 \left(- \frac{3 \sqrt{5}}{155} - \frac{1}{62}\right)^{2}}{9} \right)} + \frac{\log{\left(7 \right)}}{31} - \left(- \frac{1}{62} + \frac{3 \sqrt{5}}{155}\right) \left(\log{\left(- \frac{31 \sqrt{5}}{3} - \frac{163370 \left(- \frac{1}{62} + \frac{3 \sqrt{5}}{155}\right)^{2}}{9} + \frac{697}{18} \right)} + i \pi\right) + \left(- \frac{1}{62} + \frac{3 \sqrt{5}}{155}\right) \left(\log{\left(- \frac{31 \sqrt{5}}{3} - \frac{163370 \left(- \frac{1}{62} + \frac{3 \sqrt{5}}{155}\right)^{2}}{9} + \frac{679}{18} \right)} + i \pi\right)$$
=
=
/ 2\ / / 2 \\ / 2\ / / 2 \\
| / ___\ | | | / ___\ || | / ___\ | | | / ___\ ||
| | 1 3*\/ 5 | | | | | 1 3*\/ 5 | || | | 1 3*\/ 5 | | | | | 1 3*\/ 5 | ||
/ ___\ | ___ 163370*|- -- - -------| | / ___\ | | 163370*|- -- + -------| ___|| / ___\ | ___ 163370*|- -- - -------| | / ___\ | | 163370*|- -- + -------| ___||
log(6) log(7) | 1 3*\/ 5 | | 679 31*\/ 5 \ 62 155 / | | 1 3*\/ 5 | | |679 \ 62 155 / 31*\/ 5 || | 1 3*\/ 5 | | 697 31*\/ 5 \ 62 155 / | | 1 3*\/ 5 | | |697 \ 62 155 / 31*\/ 5 ||
- ------ + ------ + |- -- - -------|*log|- --- - -------- + ------------------------| + |- -- + -------|*|pi*I + log|--- - ------------------------ - --------|| - |- -- - -------|*log|- --- - -------- + ------------------------| - |- -- + -------|*|pi*I + log|--- - ------------------------ - --------||
31 31 \ 62 155 / \ 18 3 9 / \ 62 155 / \ \ 18 9 3 // \ 62 155 / \ 18 3 9 / \ 62 155 / \ \ 18 9 3 //
$$\left(- \frac{3 \sqrt{5}}{155} - \frac{1}{62}\right) \log{\left(- \frac{679}{18} - \frac{31 \sqrt{5}}{3} + \frac{163370 \left(- \frac{3 \sqrt{5}}{155} - \frac{1}{62}\right)^{2}}{9} \right)} - \frac{\log{\left(6 \right)}}{31} - \left(- \frac{3 \sqrt{5}}{155} - \frac{1}{62}\right) \log{\left(- \frac{697}{18} - \frac{31 \sqrt{5}}{3} + \frac{163370 \left(- \frac{3 \sqrt{5}}{155} - \frac{1}{62}\right)^{2}}{9} \right)} + \frac{\log{\left(7 \right)}}{31} - \left(- \frac{1}{62} + \frac{3 \sqrt{5}}{155}\right) \left(\log{\left(- \frac{31 \sqrt{5}}{3} - \frac{163370 \left(- \frac{1}{62} + \frac{3 \sqrt{5}}{155}\right)^{2}}{9} + \frac{697}{18} \right)} + i \pi\right) + \left(- \frac{1}{62} + \frac{3 \sqrt{5}}{155}\right) \left(\log{\left(- \frac{31 \sqrt{5}}{3} - \frac{163370 \left(- \frac{1}{62} + \frac{3 \sqrt{5}}{155}\right)^{2}}{9} + \frac{679}{18} \right)} + i \pi\right)$$
-log(6)/31 + log(7)/31 + (-1/62 - 3*sqrt(5)/155)*log(-679/18 - 31*sqrt(5)/3 + 163370*(-1/62 - 3*sqrt(5)/155)^2/9) + (-1/62 + 3*sqrt(5)/155)*(pi*i + log(679/18 - 163370*(-1/62 + 3*sqrt(5)/155)^2/9 - 31*sqrt(5)/3)) - (-1/62 - 3*sqrt(5)/155)*log(-697/18 - 31*sqrt(5)/3 + 163370*(-1/62 - 3*sqrt(5)/155)^2/9) - (-1/62 + 3*sqrt(5)/155)*(pi*i + log(697/18 - 163370*(-1/62 + 3*sqrt(5)/155)^2/9 - 31*sqrt(5)/3))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.