Sr Examen
Integral de sqrt(x)/(x-2)/(1/3)dx dx
Solución
Ha introducido
[src]
1 / | | / ___\ | |\/ x | | |-----| | \x - 2/ | ------- dx | 1/3 | / 0
1
/
|
| / ___\
| |\/ x |
| |-----|
| \x - 2/
| ------- dx
| 1/3
|
/
0
Integral((sqrt(x)/(x - 2))/(1/3), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ // / ___ ___\ \
| || ___ |\/ 2 *\/ x | |
| / ___\ ||-\/ 2 *acoth|-----------| |
| |\/ x | || \ 2 / |
| |-----| ||-------------------------- for x > 2|
| \x - 2/ ___ || 2 |
| ------- dx = C + 6*\/ x + 12*|< |
| 1/3 || / ___ ___\ |
| || ___ |\/ 2 *\/ x | |
/ ||-\/ 2 *atanh|-----------| |
|| \ 2 / |
||-------------------------- for x < 2|
\\ 2 /
/ // / ___ ___\ \
| || ___ |\/ 2 *\/ x | |
| / ___\ ||-\/ 2 *acoth|-----------| |
| |\/ x | || \ 2 / |
| |-----| ||-------------------------- for x > 2|
| \x - 2/ ___ || 2 |
| ------- dx = C + 6*\/ x + 12*|< |
| 1/3 || / ___ ___\ |
| || ___ |\/ 2 *\/ x | |
/ ||-\/ 2 *atanh|-----------| |
|| \ 2 / |
||-------------------------- for x < 2|
\\ 2 /
Gráfica
Respuesta
[src]
___ / / ___\\ ___ / ___\ ___ / / ___\\ ___ / ___\ 6 - 3*\/ 2 *\pi*I + log\\/ 2 // - 3*\/ 2 *log\1 + \/ 2 / + 3*\/ 2 *\pi*I + log\-1 + \/ 2 // + 3*\/ 2 *log\\/ 2 /
$$- 3 \sqrt{2} \log{\left(1 + \sqrt{2} \right)} + 3 \sqrt{2} \log{\left(\sqrt{2} \right)} + 6 - 3 \sqrt{2} \left(\log{\left(\sqrt{2} \right)} + i \pi\right) + 3 \sqrt{2} \left(\log{\left(-1 + \sqrt{2} \right)} + i \pi\right)$$
=
=
___ / / ___\\ ___ / ___\ ___ / / ___\\ ___ / ___\ 6 - 3*\/ 2 *\pi*I + log\\/ 2 // - 3*\/ 2 *log\1 + \/ 2 / + 3*\/ 2 *\pi*I + log\-1 + \/ 2 // + 3*\/ 2 *log\\/ 2 /
$$- 3 \sqrt{2} \log{\left(1 + \sqrt{2} \right)} + 3 \sqrt{2} \log{\left(\sqrt{2} \right)} + 6 - 3 \sqrt{2} \left(\log{\left(\sqrt{2} \right)} + i \pi\right) + 3 \sqrt{2} \left(\log{\left(-1 + \sqrt{2} \right)} + i \pi\right)$$
6 - 3*sqrt(2)*(pi*i + log(sqrt(2))) - 3*sqrt(2)*log(1 + sqrt(2)) + 3*sqrt(2)*(pi*i + log(-1 + sqrt(2))) + 3*sqrt(2)*log(sqrt(2))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.