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