Sr Examen
Integral de dx/(a+bx)^c dx
Solución
Ha introducido
[src]
1 / | | 1 | ---------- dx | c | (a + b*x) | / 0
$$\int\limits_{0}^{1} \frac{1}{\left(a + b x\right)^{c}}\, dx$$
Integral(1/((a + b*x)^c), (x, 0, 1))
Respuesta (Indefinida)
[src]
// x \
|| - for And(b = 0, c = 1)|
|| a |
|| |
|| -c |
/ || x*a for b = 0 |
| || |
| 1 || / a\ |
| ---------- dx = C + |< log|x + -| |
| c || \ b/ |
| (a + b*x) || ---------- for c = 1 |
| || b |
/ || |
|| a b*x |
||- ------------------------------- - ------------------------------- otherwise |
|| c c c c |
\\ - b*(a + b*x) + b*c*(a + b*x) - b*(a + b*x) + b*c*(a + b*x) /
$$\int \frac{1}{\left(a + b x\right)^{c}}\, dx = C + \begin{cases} \frac{x}{a} & \text{for}\: b = 0 \wedge c = 1 \\a^{- c} x & \text{for}\: b = 0 \\\frac{\log{\left(\frac{a}{b} + x \right)}}{b} & \text{for}\: c = 1 \\- \frac{a}{b c \left(a + b x\right)^{c} - b \left(a + b x\right)^{c}} - \frac{b x}{b c \left(a + b x\right)^{c} - b \left(a + b x\right)^{c}} & \text{otherwise} \end{cases}$$
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.