Sr Examen
Integral de 1/((x-3)((x)^(1/2)+1)) dx
Solución
Ha introducido
[src]
9 / | | 1 | ------------------- dx | / ___ \ | (x - 3)*\\/ x + 1/ | / 4
$$\int\limits_{4}^{9} \frac{1}{\left(\sqrt{x} + 1\right) \left(x - 3\right)}\, dx$$
Integral(1/((x - 3)*(sqrt(x) + 1)), (x, 4, 9))
Respuesta (Indefinida)
[src]
// / ___ ___\ \
|| ___ |\/ 3 *\/ x | |
||-\/ 3 *acoth|-----------| |
/ || \ 3 / |
| ||-------------------------- for x > 3|
| 1 || 3 | log(-3 + x) / ___\
| ------------------- dx = C + 3*|< | - ----------- + log\1 + \/ x /
| / ___ \ || / ___ ___\ | 2
| (x - 3)*\\/ x + 1/ || ___ |\/ 3 *\/ x | |
| ||-\/ 3 *atanh|-----------| |
/ || \ 3 / |
||-------------------------- for x < 3|
\\ 3 /
$$\int \frac{1}{\left(\sqrt{x} + 1\right) \left(x - 3\right)}\, dx = C + 3 \left(\begin{cases} - \frac{\sqrt{3} \operatorname{acoth}{\left(\frac{\sqrt{3} \sqrt{x}}{3} \right)}}{3} & \text{for}\: x > 3 \\- \frac{\sqrt{3} \operatorname{atanh}{\left(\frac{\sqrt{3} \sqrt{x}}{3} \right)}}{3} & \text{for}\: x < 3 \end{cases}\right) + \log{\left(\sqrt{x} + 1 \right)} - \frac{\log{\left(x - 3 \right)}}{2}$$
Gráfica
Respuesta
[src]
/ ___\ / ___\ / ___\ / ___\ ___ / ___\ ___ / ___\ ___ / ___\ ___ / ___\
log\2 + \/ 3 / log\2 - \/ 3 / log\3 + \/ 3 / log\3 - \/ 3 / \/ 3 *log\2 + \/ 3 / \/ 3 *log\3 - \/ 3 / \/ 3 *log\2 - \/ 3 / \/ 3 *log\3 + \/ 3 /
-------------- + -------------- - log(3) - -------------- - -------------- + -------------------- + -------------------- - -------------------- - -------------------- + log(4)
2 2 2 2 2 2 2 2
$$- \frac{\sqrt{3} \log{\left(\sqrt{3} + 3 \right)}}{2} - \log{\left(3 \right)} - \frac{\log{\left(\sqrt{3} + 3 \right)}}{2} + \frac{\log{\left(2 - \sqrt{3} \right)}}{2} - \frac{\log{\left(3 - \sqrt{3} \right)}}{2} + \frac{\sqrt{3} \log{\left(3 - \sqrt{3} \right)}}{2} + \frac{\log{\left(\sqrt{3} + 2 \right)}}{2} + \frac{\sqrt{3} \log{\left(\sqrt{3} + 2 \right)}}{2} - \frac{\sqrt{3} \log{\left(2 - \sqrt{3} \right)}}{2} + \log{\left(4 \right)}$$
=
=
/ ___\ / ___\ / ___\ / ___\ ___ / ___\ ___ / ___\ ___ / ___\ ___ / ___\
log\2 + \/ 3 / log\2 - \/ 3 / log\3 + \/ 3 / log\3 - \/ 3 / \/ 3 *log\2 + \/ 3 / \/ 3 *log\3 - \/ 3 / \/ 3 *log\2 - \/ 3 / \/ 3 *log\3 + \/ 3 /
-------------- + -------------- - log(3) - -------------- - -------------- + -------------------- + -------------------- - -------------------- - -------------------- + log(4)
2 2 2 2 2 2 2 2
$$- \frac{\sqrt{3} \log{\left(\sqrt{3} + 3 \right)}}{2} - \log{\left(3 \right)} - \frac{\log{\left(\sqrt{3} + 3 \right)}}{2} + \frac{\log{\left(2 - \sqrt{3} \right)}}{2} - \frac{\log{\left(3 - \sqrt{3} \right)}}{2} + \frac{\sqrt{3} \log{\left(3 - \sqrt{3} \right)}}{2} + \frac{\log{\left(\sqrt{3} + 2 \right)}}{2} + \frac{\sqrt{3} \log{\left(\sqrt{3} + 2 \right)}}{2} - \frac{\sqrt{3} \log{\left(2 - \sqrt{3} \right)}}{2} + \log{\left(4 \right)}$$
log(2 + sqrt(3))/2 + log(2 - sqrt(3))/2 - log(3) - log(3 + sqrt(3))/2 - log(3 - sqrt(3))/2 + sqrt(3)*log(2 + sqrt(3))/2 + sqrt(3)*log(3 - sqrt(3))/2 - sqrt(3)*log(2 - sqrt(3))/2 - sqrt(3)*log(3 + sqrt(3))/2 + log(4)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.