Sr Examen
Integral de sin(t)/(1-kcos(t)) dt
Solución
Ha introducido
[src]
pi / | | sin(t) | ------------ dt | 1 - k*cos(t) | / 0
$$\int\limits_{0}^{\pi} \frac{\sin{\left(t \right)}}{- k \cos{\left(t \right)} + 1}\, dt$$
Integral(sin(t)/(1 - k*cos(t)), (t, 0, pi))
Respuesta (Indefinida)
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/ | //log(1 - k*cos(t)) \ | sin(t) ||----------------- for k != 0| | ------------ dt = C + |< k | | 1 - k*cos(t) || | | \\ -cos(t) otherwise / /
$$\int \frac{\sin{\left(t \right)}}{- k \cos{\left(t \right)} + 1}\, dt = C + \begin{cases} \frac{\log{\left(- k \cos{\left(t \right)} + 1 \right)}}{k} & \text{for}\: k \neq 0 \\- \cos{\left(t \right)} & \text{otherwise} \end{cases}$$
Respuesta
[src]
/ / 1\ / 1\ |log|-1 - -| log|1 - -| | \ k/ \ k/ <----------- - ---------- for And(k > -oo, k < oo, k != 0) | k k | \ 2 otherwise
$$\begin{cases} \frac{\log{\left(-1 - \frac{1}{k} \right)}}{k} - \frac{\log{\left(1 - \frac{1}{k} \right)}}{k} & \text{for}\: k > -\infty \wedge k < \infty \wedge k \neq 0 \\2 & \text{otherwise} \end{cases}$$
=
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/ / 1\ / 1\ |log|-1 - -| log|1 - -| | \ k/ \ k/ <----------- - ---------- for And(k > -oo, k < oo, k != 0) | k k | \ 2 otherwise
$$\begin{cases} \frac{\log{\left(-1 - \frac{1}{k} \right)}}{k} - \frac{\log{\left(1 - \frac{1}{k} \right)}}{k} & \text{for}\: k > -\infty \wedge k < \infty \wedge k \neq 0 \\2 & \text{otherwise} \end{cases}$$
Piecewise((log(-1 - 1/k)/k - log(1 - 1/k)/k, (k > -oo)∧(k < oo)∧(Ne(k, 0))), (2, True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.