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