Sr Examen
Integral de (x+1)/(x*sqrt(x+2)) dx
Solución
Ha introducido
[src]
1 / | | x + 1 | ----------- dx | _______ | x*\/ x + 2 | / 0
$$\int\limits_{0}^{1} \frac{x + 1}{x \sqrt{x + 2}}\, dx$$
Integral((x + 1)/((x*sqrt(x + 2))), (x, 0, 1))
Respuesta (Indefinida)
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// / ___ \ \
|| ___ | \/ 2 | |
||-\/ 2 *acoth|---------| |
|| | _______| |
/ || \\/ x + 2 / 1 |
| ||------------------------ for ----- > 1/2|
| x + 1 _______ || 2 x + 2 |
| ----------- dx = C + 2*\/ x + 2 + 2*|< |
| _______ || / ___ \ |
| x*\/ x + 2 || ___ | \/ 2 | |
| ||-\/ 2 *atanh|---------| |
/ || | _______| |
|| \\/ x + 2 / 1 |
||------------------------ for ----- < 1/2|
\\ 2 x + 2 /
$$\int \frac{x + 1}{x \sqrt{x + 2}}\, dx = C + 2 \sqrt{x + 2} + 2 \left(\begin{cases} - \frac{\sqrt{2} \operatorname{acoth}{\left(\frac{\sqrt{2}}{\sqrt{x + 2}} \right)}}{2} & \text{for}\: \frac{1}{x + 2} > \frac{1}{2} \\- \frac{\sqrt{2} \operatorname{atanh}{\left(\frac{\sqrt{2}}{\sqrt{x + 2}} \right)}}{2} & \text{for}\: \frac{1}{x + 2} < \frac{1}{2} \end{cases}\right)$$
Respuesta
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/ ___\
___ |\/ 6 |
oo - \/ 2 *atanh|-----|
\ 3 /
$$- \sqrt{2} \operatorname{atanh}{\left(\frac{\sqrt{6}}{3} \right)} + \infty$$
=
=
/ ___\
___ |\/ 6 |
oo - \/ 2 *atanh|-----|
\ 3 /
$$- \sqrt{2} \operatorname{atanh}{\left(\frac{\sqrt{6}}{3} \right)} + \infty$$
oo - sqrt(2)*atanh(sqrt(6)/3)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.