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