Sr Examen
Integral de x^m/sqrt(n+m+x^(m+1)) dx
Solución
Ha introducido
[src]
1 / | | m | x | ------------------- dx | ________________ | / m + 1 | \/ n + m + x | / 0
$$\int\limits_{0}^{1} \frac{x^{m}}{\sqrt{x^{m + 1} + \left(m + n\right)}}\, dx$$
Integral(x^m/sqrt(n + m + x^(m + 1)), (x, 0, 1))
Respuesta (Indefinida)
[src]
// ________________ \
|| / m + 1 |
||2*\/ n + m + x |
||--------------------- for 1 + m != 0|
/ || 1 + m |
| || |
| m ||/ 1 + m |
| x |||x |
| ------------------- dx = C + |<|------ for m != -1 |
| ________________ ||<1 + m |
| / m + 1 ||| |
| \/ n + m + x |||log(x) otherwise |
| ||\ |
/ ||-------------------- otherwise |
|| ___ |
|| \/ n |
\\ /
$$\int \frac{x^{m}}{\sqrt{x^{m + 1} + \left(m + n\right)}}\, dx = C + \begin{cases} \frac{2 \sqrt{x^{m + 1} + \left(m + n\right)}}{m + 1} & \text{for}\: m + 1 \neq 0 \\\frac{\begin{cases} \frac{x^{m + 1}}{m + 1} & \text{for}\: m \neq -1 \\\log{\left(x \right)} & \text{otherwise} \end{cases}}{\sqrt{n}} & \text{otherwise} \end{cases}$$
Respuesta
[src]
_______________________
/ 1 ___________________
___________________ 2* / 1 + ----------------- *\/ polar_lift(m + n)
2*\/ polar_lift(m + n) \/ polar_lift(m + n)
- ----------------------- + ---------------------------------------------------
1 + m 1 + m
$$\frac{2 \sqrt{1 + \frac{1}{\operatorname{polar\_lift}{\left(m + n \right)}}} \sqrt{\operatorname{polar\_lift}{\left(m + n \right)}}}{m + 1} - \frac{2 \sqrt{\operatorname{polar\_lift}{\left(m + n \right)}}}{m + 1}$$
=
=
_______________________
/ 1 ___________________
___________________ 2* / 1 + ----------------- *\/ polar_lift(m + n)
2*\/ polar_lift(m + n) \/ polar_lift(m + n)
- ----------------------- + ---------------------------------------------------
1 + m 1 + m
$$\frac{2 \sqrt{1 + \frac{1}{\operatorname{polar\_lift}{\left(m + n \right)}}} \sqrt{\operatorname{polar\_lift}{\left(m + n \right)}}}{m + 1} - \frac{2 \sqrt{\operatorname{polar\_lift}{\left(m + n \right)}}}{m + 1}$$
-2*sqrt(polar_lift(m + n))/(1 + m) + 2*sqrt(1 + 1/polar_lift(m + n))*sqrt(polar_lift(m + n))/(1 + m)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.