Sr Examen
Integral de (2-x)^0,5/(x+5) dx
Solución
Ha introducido
[src]
1 / | | _______ | \/ 2 - x | --------- dx | x + 5 | / 0
$$\int\limits_{0}^{1} \frac{\sqrt{2 - x}}{x + 5}\, dx$$
Integral(sqrt(2 - x)/(x + 5), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / ___ _______\ \
|| ___ |\/ 7 *\/ 2 - x | |
/ ||-\/ 7 *acoth|---------------| |
| || \ 7 / |
| _______ ||------------------------------ for -2 + x < -7|
| \/ 2 - x _______ || 7 |
| --------- dx = C + 2*\/ 2 - x + 14*|< |
| x + 5 || / ___ _______\ |
| || ___ |\/ 7 *\/ 2 - x | |
/ ||-\/ 7 *atanh|---------------| |
|| \ 7 / |
||------------------------------ for -2 + x > -7|
\\ 7 /
$$\int \frac{\sqrt{2 - x}}{x + 5}\, dx = C + 2 \sqrt{2 - x} + 14 \left(\begin{cases} - \frac{\sqrt{7} \operatorname{acoth}{\left(\frac{\sqrt{7} \sqrt{2 - x}}{7} \right)}}{7} & \text{for}\: x - 2 < -7 \\- \frac{\sqrt{7} \operatorname{atanh}{\left(\frac{\sqrt{7} \sqrt{2 - x}}{7} \right)}}{7} & \text{for}\: x - 2 > -7 \end{cases}\right)$$
Gráfica
Respuesta
[src]
/ ___\ / ____\
___ ___ ___ ___ | \/ 7 | ___ | \/ 14 |
2 - 2*\/ 2 + \/ 7 *log(6) - \/ 7 *log(5) - 2*\/ 7 *log|1 + -----| + 2*\/ 7 *log|1 + ------|
\ 7 / \ 7 /
$$- \sqrt{7} \log{\left(5 \right)} - 2 \sqrt{2} - 2 \sqrt{7} \log{\left(\frac{\sqrt{7}}{7} + 1 \right)} + 2 + 2 \sqrt{7} \log{\left(\frac{\sqrt{14}}{7} + 1 \right)} + \sqrt{7} \log{\left(6 \right)}$$
=
=
/ ___\ / ____\
___ ___ ___ ___ | \/ 7 | ___ | \/ 14 |
2 - 2*\/ 2 + \/ 7 *log(6) - \/ 7 *log(5) - 2*\/ 7 *log|1 + -----| + 2*\/ 7 *log|1 + ------|
\ 7 / \ 7 /
$$- \sqrt{7} \log{\left(5 \right)} - 2 \sqrt{2} - 2 \sqrt{7} \log{\left(\frac{\sqrt{7}}{7} + 1 \right)} + 2 + 2 \sqrt{7} \log{\left(\frac{\sqrt{14}}{7} + 1 \right)} + \sqrt{7} \log{\left(6 \right)}$$
2 - 2*sqrt(2) + sqrt(7)*log(6) - sqrt(7)*log(5) - 2*sqrt(7)*log(1 + sqrt(7)/7) + 2*sqrt(7)*log(1 + sqrt(14)/7)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.