Sr Examen
Integral de (1+(x+1)^(1/3))/(x+(x+1)^(1/2)) dx
Solución
Ha introducido
[src]
0 / | | 3 _______ | 1 + \/ x + 1 | ------------- dx | _______ | x + \/ x + 1 | / 0
$$\int\limits_{0}^{0} \frac{\sqrt[3]{x + 1} + 1}{x + \sqrt{x + 1}}\, dx$$
Integral((1 + (x + 1)^(1/3))/(x + sqrt(x + 1)), (x, 0, 0))
Respuesta (Indefinida)
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// / ___ /1 _______\\ \
|| |2*\/ 5 *|- + \/ x + 1 || |
|| ___ | \2 /| |
/ ||-\/ 5 *acoth|-----------------------| 2 | /
| || \ 5 / /1 _______\ | |
| 3 _______ ||-------------------------------------- for |- + \/ x + 1 | > 5/4| | 3 _______
| 1 + \/ x + 1 || 10 \2 / | | \/ 1 + x / _______\
| ------------- dx = C - 4*|< | + | ------------- dx + log\x + \/ x + 1 /
| _______ || / ___ /1 _______\\ | | _______
| x + \/ x + 1 || |2*\/ 5 *|- + \/ x + 1 || | | x + \/ 1 + x
| || ___ | \2 /| | |
/ ||-\/ 5 *atanh|-----------------------| 2 | /
|| \ 5 / /1 _______\ |
||-------------------------------------- for |- + \/ x + 1 | < 5/4|
\\ 10 \2 / /
$$\int \frac{\sqrt[3]{x + 1} + 1}{x + \sqrt{x + 1}}\, dx = C - 4 \left(\begin{cases} - \frac{\sqrt{5} \operatorname{acoth}{\left(\frac{2 \sqrt{5} \left(\sqrt{x + 1} + \frac{1}{2}\right)}{5} \right)}}{10} & \text{for}\: \left(\sqrt{x + 1} + \frac{1}{2}\right)^{2} > \frac{5}{4} \\- \frac{\sqrt{5} \operatorname{atanh}{\left(\frac{2 \sqrt{5} \left(\sqrt{x + 1} + \frac{1}{2}\right)}{5} \right)}}{10} & \text{for}\: \left(\sqrt{x + 1} + \frac{1}{2}\right)^{2} < \frac{5}{4} \end{cases}\right) + \log{\left(x + \sqrt{x + 1} \right)} + \int \frac{\sqrt[3]{x + 1}}{x + \sqrt{x + 1}}\, dx$$
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.