Sr Examen
Integral de (dx)/x^(1/n) dx
Solución
Ha introducido
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1 / | | 1 | ----- dx | n ___ | \/ x | / 0
$$\int\limits_{0}^{1} \frac{1}{x^{\frac{1}{n}}}\, dx$$
Integral(1/(x^(1/n)), (x, 0, 1))
Respuesta (Indefinida)
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/ // n*x \ | ||----------------- for n != 1| | 1 || n ___ n ___ | | ----- dx = C + |<- \/ x + n*\/ x | | n ___ || | | \/ x || log(x) otherwise | | \\ / /
$$\int \frac{1}{x^{\frac{1}{n}}}\, dx = C + \begin{cases} \frac{n x}{n x^{\frac{1}{n}} - x^{\frac{1}{n}}} & \text{for}\: n \neq 1 \\\log{\left(x \right)} & \text{otherwise} \end{cases}$$
Respuesta
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/ 1 | 1 - - | n | 1 0 |----- - ------ for Or(And(n > 0, n < 1), n > 1, n < 0) < 1 1 |1 - - 1 - - | n n | | oo otherwise \
$$\begin{cases} - \frac{0^{1 - \frac{1}{n}}}{1 - \frac{1}{n}} + \frac{1}{1 - \frac{1}{n}} & \text{for}\: \left(n > 0 \wedge n < 1\right) \vee n > 1 \vee n < 0 \\\infty & \text{otherwise} \end{cases}$$
=
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/ 1 | 1 - - | n | 1 0 |----- - ------ for Or(And(n > 0, n < 1), n > 1, n < 0) < 1 1 |1 - - 1 - - | n n | | oo otherwise \
$$\begin{cases} - \frac{0^{1 - \frac{1}{n}}}{1 - \frac{1}{n}} + \frac{1}{1 - \frac{1}{n}} & \text{for}\: \left(n > 0 \wedge n < 1\right) \vee n > 1 \vee n < 0 \\\infty & \text{otherwise} \end{cases}$$
Piecewise((1/(1 - 1/n) - 0^(1 - 1/n)/(1 - 1/n), (n > 1)∨(n < 0)∨((n > 0)∧(n < 1))), (oo, True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.