Sr Examen
Integral de (3-x)/(√16+16*x-x^2) dx
Solución
Ha introducido
[src]
1 / | | 3 - x | ------------------ dx | ____ 2 | \/ 16 + 16*x - x | / 0
$$\int\limits_{0}^{1} \frac{3 - x}{- x^{2} + \left(16 x + \sqrt{16}\right)}\, dx$$
Integral((3 - x)/(sqrt(16) + 16*x - x^2), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / ____ \ \
|| ____ |\/ 17 *(-8 + x)| |
||-\/ 17 *acoth|---------------| |
/ || \ 34 / 2 |
| / ____ 2 \ ||------------------------------- for (-8 + x) > 68|
| 3 - x log\\/ 16 - x + 16*x/ || 34 |
| ------------------ dx = C + ----------------------- + 5*|< |
| ____ 2 2 || / ____ \ |
| \/ 16 + 16*x - x || ____ |\/ 17 *(-8 + x)| |
| ||-\/ 17 *atanh|---------------| |
/ || \ 34 / 2 |
||------------------------------- for (-8 + x) < 68|
\\ 34 /
$$\int \frac{3 - x}{- x^{2} + \left(16 x + \sqrt{16}\right)}\, dx = C + 5 \left(\begin{cases} - \frac{\sqrt{17} \operatorname{acoth}{\left(\frac{\sqrt{17} \left(x - 8\right)}{34} \right)}}{34} & \text{for}\: \left(x - 8\right)^{2} > 68 \\- \frac{\sqrt{17} \operatorname{atanh}{\left(\frac{\sqrt{17} \left(x - 8\right)}{34} \right)}}{34} & \text{for}\: \left(x - 8\right)^{2} < 68 \end{cases}\right) + \frac{\log{\left(- x^{2} + 16 x + \sqrt{16} \right)}}{2}$$
Gráfica
Respuesta
[src]
/ ____\ / ____\ / ____\ / ____\ |1 5*\/ 17 | / ____\ |1 5*\/ 17 | / / ____\\ |1 5*\/ 17 | / ____\ |1 5*\/ 17 | / / ____\\ |- - --------|*log\-7 + 2*\/ 17 / + |- + --------|*\pi*I + log\7 + 2*\/ 17 // - |- - --------|*log\-8 + 2*\/ 17 / - |- + --------|*\pi*I + log\8 + 2*\/ 17 // \2 68 / \2 68 / \2 68 / \2 68 /
$$\left(\frac{1}{2} - \frac{5 \sqrt{17}}{68}\right) \log{\left(-7 + 2 \sqrt{17} \right)} - \left(\frac{1}{2} - \frac{5 \sqrt{17}}{68}\right) \log{\left(-8 + 2 \sqrt{17} \right)} - \left(\frac{5 \sqrt{17}}{68} + \frac{1}{2}\right) \left(\log{\left(8 + 2 \sqrt{17} \right)} + i \pi\right) + \left(\frac{5 \sqrt{17}}{68} + \frac{1}{2}\right) \left(\log{\left(7 + 2 \sqrt{17} \right)} + i \pi\right)$$
=
=
/ ____\ / ____\ / ____\ / ____\ |1 5*\/ 17 | / ____\ |1 5*\/ 17 | / / ____\\ |1 5*\/ 17 | / ____\ |1 5*\/ 17 | / / ____\\ |- - --------|*log\-7 + 2*\/ 17 / + |- + --------|*\pi*I + log\7 + 2*\/ 17 // - |- - --------|*log\-8 + 2*\/ 17 / - |- + --------|*\pi*I + log\8 + 2*\/ 17 // \2 68 / \2 68 / \2 68 / \2 68 /
$$\left(\frac{1}{2} - \frac{5 \sqrt{17}}{68}\right) \log{\left(-7 + 2 \sqrt{17} \right)} - \left(\frac{1}{2} - \frac{5 \sqrt{17}}{68}\right) \log{\left(-8 + 2 \sqrt{17} \right)} - \left(\frac{5 \sqrt{17}}{68} + \frac{1}{2}\right) \left(\log{\left(8 + 2 \sqrt{17} \right)} + i \pi\right) + \left(\frac{5 \sqrt{17}}{68} + \frac{1}{2}\right) \left(\log{\left(7 + 2 \sqrt{17} \right)} + i \pi\right)$$
(1/2 - 5*sqrt(17)/68)*log(-7 + 2*sqrt(17)) + (1/2 + 5*sqrt(17)/68)*(pi*i + log(7 + 2*sqrt(17))) - (1/2 - 5*sqrt(17)/68)*log(-8 + 2*sqrt(17)) - (1/2 + 5*sqrt(17)/68)*(pi*i + log(8 + 2*sqrt(17)))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.