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