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