Sr Examen
Integral de sqrt(x)/(6-5x) dx
Solución
Ha introducido
[src]
1 / | | ___ | \/ x | ------- dx | 6 - 5*x | / 0
$$\int\limits_{0}^{1} \frac{\sqrt{x}}{6 - 5 x}\, dx$$
Integral(sqrt(x)/(6 - 5*x), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / ____ ___\ \
|| ____ |\/ 30 *\/ x | |
||-\/ 30 *acoth|------------| |
|| \ 6 / |
||---------------------------- for x > 6/5|
|| 30 |
12*|< |
|| / ____ ___\ |
|| ____ |\/ 30 *\/ x | |
/ ||-\/ 30 *atanh|------------| |
| || \ 6 / |
| ___ ||---------------------------- for x < 6/5| ___
| \/ x \\ 30 / 2*\/ x
| ------- dx = C - ----------------------------------------------- - -------
| 6 - 5*x 5 5
|
/
$$\int \frac{\sqrt{x}}{6 - 5 x}\, dx = C - \frac{2 \sqrt{x}}{5} - \frac{12 \left(\begin{cases} - \frac{\sqrt{30} \operatorname{acoth}{\left(\frac{\sqrt{30} \sqrt{x}}{6} \right)}}{30} & \text{for}\: x > \frac{6}{5} \\- \frac{\sqrt{30} \operatorname{atanh}{\left(\frac{\sqrt{30} \sqrt{x}}{6} \right)}}{30} & \text{for}\: x < \frac{6}{5} \end{cases}\right)}{5}$$
Gráfica
Respuesta
[src]
/ / ____\\ / ____\ / / ____\\ / ____\
____ | | \/ 30 || ____ |\/ 30 | ____ | |\/ 30 || ____ | \/ 30 |
\/ 30 *|pi*I + log|-1 + ------|| \/ 30 *log|------| \/ 30 *|pi*I + log|------|| \/ 30 *log|1 + ------|
2 \ \ 5 // \ 5 / \ \ 5 // \ 5 /
- - - -------------------------------- - ------------------ + --------------------------- + ----------------------
5 25 25 25 25
$$- \frac{2}{5} - \frac{\sqrt{30} \log{\left(\frac{\sqrt{30}}{5} \right)}}{25} + \frac{\sqrt{30} \log{\left(1 + \frac{\sqrt{30}}{5} \right)}}{25} - \frac{\sqrt{30} \left(\log{\left(-1 + \frac{\sqrt{30}}{5} \right)} + i \pi\right)}{25} + \frac{\sqrt{30} \left(\log{\left(\frac{\sqrt{30}}{5} \right)} + i \pi\right)}{25}$$
=
=
/ / ____\\ / ____\ / / ____\\ / ____\
____ | | \/ 30 || ____ |\/ 30 | ____ | |\/ 30 || ____ | \/ 30 |
\/ 30 *|pi*I + log|-1 + ------|| \/ 30 *log|------| \/ 30 *|pi*I + log|------|| \/ 30 *log|1 + ------|
2 \ \ 5 // \ 5 / \ \ 5 // \ 5 /
- - - -------------------------------- - ------------------ + --------------------------- + ----------------------
5 25 25 25 25
$$- \frac{2}{5} - \frac{\sqrt{30} \log{\left(\frac{\sqrt{30}}{5} \right)}}{25} + \frac{\sqrt{30} \log{\left(1 + \frac{\sqrt{30}}{5} \right)}}{25} - \frac{\sqrt{30} \left(\log{\left(-1 + \frac{\sqrt{30}}{5} \right)} + i \pi\right)}{25} + \frac{\sqrt{30} \left(\log{\left(\frac{\sqrt{30}}{5} \right)} + i \pi\right)}{25}$$
-2/5 - sqrt(30)*(pi*i + log(-1 + sqrt(30)/5))/25 - sqrt(30)*log(sqrt(30)/5)/25 + sqrt(30)*(pi*i + log(sqrt(30)/5))/25 + sqrt(30)*log(1 + sqrt(30)/5)/25
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.