Sr Examen
Integral de cos(2ax+b) dx
Solución
Ha introducido
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2 / | | cos(2*a*x + b) dx | / 1
$$\int\limits_{1}^{2} \cos{\left(2 a x + b \right)}\, dx$$
Integral(cos((2*a)*x + b), (x, 1, 2))
Respuesta (Indefinida)
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/ //sin(2*a*x + b) \ | ||-------------- for a != 0| | cos(2*a*x + b) dx = C + |< 2*a | | || | / \\ sin(b) otherwise /
$$\int \cos{\left(2 a x + b \right)}\, dx = C + \begin{cases} \frac{\sin{\left(2 a x + b \right)}}{2 a} & \text{for}\: a \neq 0 \\\sin{\left(b \right)} & \text{otherwise} \end{cases}$$
Respuesta
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/sin(b + 4*a) sin(b + 2*a) |------------ - ------------ for And(a > -oo, a < oo, a != 0) < 2*a 2*a | \ cos(b) otherwise
$$\begin{cases} - \frac{\sin{\left(2 a + b \right)}}{2 a} + \frac{\sin{\left(4 a + b \right)}}{2 a} & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\\cos{\left(b \right)} & \text{otherwise} \end{cases}$$
=
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/sin(b + 4*a) sin(b + 2*a) |------------ - ------------ for And(a > -oo, a < oo, a != 0) < 2*a 2*a | \ cos(b) otherwise
$$\begin{cases} - \frac{\sin{\left(2 a + b \right)}}{2 a} + \frac{\sin{\left(4 a + b \right)}}{2 a} & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\\cos{\left(b \right)} & \text{otherwise} \end{cases}$$
Piecewise((sin(b + 4*a)/(2*a) - sin(b + 2*a)/(2*a), (a > -oo)∧(a < oo)∧(Ne(a, 0))), (cos(b), True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.