Sr Examen
Integral de a^(5x)+e^(5x) dx
Solución
Ha introducido
[src]
1 / | | / 5*x 5*x\ | \a + E / dx | / 0
$$\int\limits_{0}^{1} \left(a^{5 x} + e^{5 x}\right)\, dx$$
Integral(a^(5*x) + E^(5*x), (x, 0, 1))
Respuesta (Indefinida)
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/ 5*x
| a
|------ for log(a) != 0
$$\int \left(a^{5 x} + e^{5 x}\right)\, dx = C + \frac{\begin{cases} \frac{a^{5 x}}{\log{\left(a \right)}} & \text{for}\: \log{\left(a \right)} \neq 0 \\5 x & \text{otherwise} \end{cases}}{5} + \frac{e^{5 x}}{5}$$
Respuesta
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// 5 \
5 || 1 a |
1 e ||- -------- + -------- for Or(And(a >= 0, a < 1), a > 1)|
- - + -- + |< 5*log(a) 5*log(a) |
5 5 || |
|| 1 otherwise |
\\ /
$$\begin{cases} \frac{a^{5}}{5 \log{\left(a \right)}} - \frac{1}{5 \log{\left(a \right)}} & \text{for}\: \left(a \geq 0 \wedge a < 1\right) \vee a > 1 \\1 & \text{otherwise} \end{cases} - \frac{1}{5} + \frac{e^{5}}{5}$$
=
=
// 5 \
5 || 1 a |
1 e ||- -------- + -------- for Or(And(a >= 0, a < 1), a > 1)|
- - + -- + |< 5*log(a) 5*log(a) |
5 5 || |
|| 1 otherwise |
\\ /
$$\begin{cases} \frac{a^{5}}{5 \log{\left(a \right)}} - \frac{1}{5 \log{\left(a \right)}} & \text{for}\: \left(a \geq 0 \wedge a < 1\right) \vee a > 1 \\1 & \text{otherwise} \end{cases} - \frac{1}{5} + \frac{e^{5}}{5}$$
-1/5 + exp(5)/5 + Piecewise((-1/(5*log(a)) + a^5/(5*log(a)), (a > 1)∨((a >= 0)∧(a < 1))), (1, True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.