Sr Examen
Integral de dx/(16*x^2-16*x+2) dx
Solución
Ha introducido
[src]
1 / | | 1 | ---------------- dx | 2 | 16*x - 16*x + 2 | / 0
$$\int\limits_{0}^{1} \frac{1}{\left(16 x^{2} - 16 x\right) + 2}\, dx$$
Integral(1/(16*x^2 - 16*x + 2), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ ___ / ___ \
|-\/ 2 *acoth\2*\/ 2 *(-1/2 + x)/ 2
|--------------------------------- for (-1/2 + x) > 1/8
| 4
<
| ___ / ___ \
/ |-\/ 2 *atanh\2*\/ 2 *(-1/2 + x)/ 2
| |--------------------------------- for (-1/2 + x) < 1/8
| 1 \ 4
| ---------------- dx = C + ---------------------------------------------------------
| 2 2
| 16*x - 16*x + 2
|
/
$$\int \frac{1}{\left(16 x^{2} - 16 x\right) + 2}\, dx = C + \frac{\begin{cases} - \frac{\sqrt{2} \operatorname{acoth}{\left(2 \sqrt{2} \left(x - \frac{1}{2}\right) \right)}}{4} & \text{for}\: \left(x - \frac{1}{2}\right)^{2} > \frac{1}{8} \\- \frac{\sqrt{2} \operatorname{atanh}{\left(2 \sqrt{2} \left(x - \frac{1}{2}\right) \right)}}{4} & \text{for}\: \left(x - \frac{1}{2}\right)^{2} < \frac{1}{8} \end{cases}}{2}$$
Gráfica
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.