Sr Examen
Integral de (x+√(2x+3))/(x-1) dx
Solución
Ha introducido
[src]
1 / | | _________ | x + \/ 2*x + 3 | --------------- dx | x - 1 | / 0
$$\int\limits_{0}^{1} \frac{x + \sqrt{2 x + 3}}{x - 1}\, dx$$
Integral((x + sqrt(2*x + 3))/(x - 1), (x, 0, 1))
Respuesta (Indefinida)
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// / ___ _________\ \
|| ___ |\/ 5 *\/ 2*x + 3 | |
/ ||-\/ 5 *acoth|-----------------| |
| || \ 5 / |
| _________ ||-------------------------------- for 2*x + 3 > 5|
| x + \/ 2*x + 3 3 _________ || 5 |
| --------------- dx = - + C + x + 2*\/ 2*x + 3 + 10*|< | + log(-2 + 2*x)
| x - 1 2 || / ___ _________\ |
| || ___ |\/ 5 *\/ 2*x + 3 | |
/ ||-\/ 5 *atanh|-----------------| |
|| \ 5 / |
||-------------------------------- for 2*x + 3 < 5|
\\ 5 /
$$\int \frac{x + \sqrt{2 x + 3}}{x - 1}\, dx = C + x + 2 \sqrt{2 x + 3} + 10 \left(\begin{cases} - \frac{\sqrt{5} \operatorname{acoth}{\left(\frac{\sqrt{5} \sqrt{2 x + 3}}{5} \right)}}{5} & \text{for}\: 2 x + 3 > 5 \\- \frac{\sqrt{5} \operatorname{atanh}{\left(\frac{\sqrt{5} \sqrt{2 x + 3}}{5} \right)}}{5} & \text{for}\: 2 x + 3 < 5 \end{cases}\right) + \log{\left(2 x - 2 \right)} + \frac{3}{2}$$
Respuesta
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/ ____\
___ |\/ 15 |
-oo - pi*I + 2*\/ 5 *atanh|------|
\ 5 /
$$-\infty + 2 \sqrt{5} \operatorname{atanh}{\left(\frac{\sqrt{15}}{5} \right)} - i \pi$$
=
=
/ ____\
___ |\/ 15 |
-oo - pi*I + 2*\/ 5 *atanh|------|
\ 5 /
$$-\infty + 2 \sqrt{5} \operatorname{atanh}{\left(\frac{\sqrt{15}}{5} \right)} - i \pi$$
-oo - pi*i + 2*sqrt(5)*atanh(sqrt(15)/5)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.