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