Sr Examen
Integral de a^x^4*x^3 dx
Solución
Ha introducido
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1 / | | / 4\ | \x / 3 | a *x dx | / 0
$$\int\limits_{0}^{1} a^{x^{4}} x^{3}\, dx$$
Integral(a^(x^4)*x^3, (x, 0, 1))
Respuesta (Indefinida)
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/ / 4\
| \x /
|a
|------ for log(a) != 0
$$\int a^{x^{4}} x^{3}\, dx = C + \frac{\begin{cases} \frac{a^{x^{4}}}{\log{\left(a \right)}} & \text{for}\: \log{\left(a \right)} \neq 0 \\x^{4} & \text{otherwise} \end{cases}}{4}$$
Respuesta
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/ 1 a |- -------- + -------- for Or(And(a >= 0, a < 1), a > 1) < 4*log(a) 4*log(a) | \ 1/4 otherwise
$$\begin{cases} \frac{a}{4 \log{\left(a \right)}} - \frac{1}{4 \log{\left(a \right)}} & \text{for}\: \left(a \geq 0 \wedge a < 1\right) \vee a > 1 \\\frac{1}{4} & \text{otherwise} \end{cases}$$
=
=
/ 1 a |- -------- + -------- for Or(And(a >= 0, a < 1), a > 1) < 4*log(a) 4*log(a) | \ 1/4 otherwise
$$\begin{cases} \frac{a}{4 \log{\left(a \right)}} - \frac{1}{4 \log{\left(a \right)}} & \text{for}\: \left(a \geq 0 \wedge a < 1\right) \vee a > 1 \\\frac{1}{4} & \text{otherwise} \end{cases}$$
Piecewise((-1/(4*log(a)) + a/(4*log(a)), (a > 1)∨((a >= 0)∧(a < 1))), (1/4, True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.