Sr Examen
Integral de 1/(sqrt2+4x-3x^2) dx
Solución
Ha introducido
[src]
0 / | | 1 | ------------------ dx | ___ 2 | \/ 2 + 4*x - 3*x | / 0
$$\int\limits_{0}^{0} \frac{1}{- 3 x^{2} + \left(4 x + \sqrt{2}\right)}\, dx$$
Integral(1/(sqrt(2) + 4*x - 3*x^2), (x, 0, 0))
Respuesta (Indefinida)
[src]
// / -2/3 + x \ \
||-acoth|----------------| |
|| | ___________| |
|| | / ___ | |
|| | / 4 \/ 2 | |
|| | / - + ----- | ___|
|| \\/ 9 3 / 2 4 \/ 2 |
||------------------------- for (-2/3 + x) > - + -----|
|| ___________ 9 3 |
|| / ___ |
/ || / 4 \/ 2 |
| || 9* / - + ----- |
| 1 || \/ 9 3 |
| ------------------ dx = C - 3*|< |
| ___ 2 || / -2/3 + x \ |
| \/ 2 + 4*x - 3*x ||-atanh|----------------| |
| || | ___________| |
/ || | / ___ | |
|| | / 4 \/ 2 | |
|| | / - + ----- | ___|
|| \\/ 9 3 / 2 4 \/ 2 |
||------------------------- for (-2/3 + x) < - + -----|
|| ___________ 9 3 |
|| / ___ |
|| / 4 \/ 2 |
|| 9* / - + ----- |
\\ \/ 9 3 /
$$\int \frac{1}{- 3 x^{2} + \left(4 x + \sqrt{2}\right)}\, dx = C - 3 \left(\begin{cases} - \frac{\operatorname{acoth}{\left(\frac{x - \frac{2}{3}}{\sqrt{\frac{4}{9} + \frac{\sqrt{2}}{3}}} \right)}}{9 \sqrt{\frac{4}{9} + \frac{\sqrt{2}}{3}}} & \text{for}\: \left(x - \frac{2}{3}\right)^{2} > \frac{4}{9} + \frac{\sqrt{2}}{3} \\- \frac{\operatorname{atanh}{\left(\frac{x - \frac{2}{3}}{\sqrt{\frac{4}{9} + \frac{\sqrt{2}}{3}}} \right)}}{9 \sqrt{\frac{4}{9} + \frac{\sqrt{2}}{3}}} & \text{for}\: \left(x - \frac{2}{3}\right)^{2} < \frac{4}{9} + \frac{\sqrt{2}}{3} \end{cases}\right)$$
Gráfica
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.