Sr Examen
Integral de (a-x)/(a+x)^3 dx
Solución
Ha introducido
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oo / | | a - x | -------- dx | 3 | (a + x) | / 1
$$\int\limits_{1}^{\infty} \frac{a - x}{\left(a + x\right)^{3}}\, dx$$
Integral((a - x)/(a + x)^3, (x, 1, oo))
Respuesta (Indefinida)
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/ | | a - x 1 a | -------- dx = C + ----- - -------- | 3 a + x 2 | (a + x) (a + x) | /
$$\int \frac{a - x}{\left(a + x\right)^{3}}\, dx = C - \frac{a}{\left(a + x\right)^{2}} + \frac{1}{a + x}$$
Respuesta
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/ 1 1 a / / 1 \ \ |- --------- - ---------- + ---------- for Or|And||arg(1 + a)| < pi, ----- != 0, |arg(1 + a)| != pi|, |arg(1 + a)| < pi| | 2*(1 + a) 2 2 \ \ 1 + a / / | 2*(1 + a) 2*(1 + a) | | oo | / < | | | a - x | | -------- dx otherwise | | 3 | | (a + x) | | | / \ 1
$$\begin{cases} \frac{a}{2 \left(a + 1\right)^{2}} - \frac{1}{2 \left(a + 1\right)} - \frac{1}{2 \left(a + 1\right)^{2}} & \text{for}\: \left(\left|{\arg{\left(a + 1 \right)}}\right| < \pi \wedge \frac{1}{a + 1} \neq 0 \wedge \left|{\arg{\left(a + 1 \right)}}\right| \neq \pi\right) \vee \left|{\arg{\left(a + 1 \right)}}\right| < \pi \\\int\limits_{1}^{\infty} \frac{a - x}{\left(a + x\right)^{3}}\, dx & \text{otherwise} \end{cases}$$
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/ 1 1 a / / 1 \ \ |- --------- - ---------- + ---------- for Or|And||arg(1 + a)| < pi, ----- != 0, |arg(1 + a)| != pi|, |arg(1 + a)| < pi| | 2*(1 + a) 2 2 \ \ 1 + a / / | 2*(1 + a) 2*(1 + a) | | oo | / < | | | a - x | | -------- dx otherwise | | 3 | | (a + x) | | | / \ 1
$$\begin{cases} \frac{a}{2 \left(a + 1\right)^{2}} - \frac{1}{2 \left(a + 1\right)} - \frac{1}{2 \left(a + 1\right)^{2}} & \text{for}\: \left(\left|{\arg{\left(a + 1 \right)}}\right| < \pi \wedge \frac{1}{a + 1} \neq 0 \wedge \left|{\arg{\left(a + 1 \right)}}\right| \neq \pi\right) \vee \left|{\arg{\left(a + 1 \right)}}\right| < \pi \\\int\limits_{1}^{\infty} \frac{a - x}{\left(a + x\right)^{3}}\, dx & \text{otherwise} \end{cases}$$
Piecewise((-1/(2*(1 + a)) - 1/(2*(1 + a)^2) + a/(2*(1 + a)^2), (Abs(arg(1 + a)) < pi)∨((Abs(arg(1 + a)) < pi)∧(Ne(1/(1 + a), 0))∧(Ne(Abs(arg(1 + a)), pi)))), (Integral((a - x)/(a + x)^3, (x, 1, oo)), True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.