Sr Examen
Integral de (x^2+2x-1)/(2x^3+3x^2-3x) dx
Solución
Ha introducido
[src]
1 / | | 2 | x + 2*x - 1 | ----------------- dx | 3 2 | 2*x + 3*x - 3*x | / 0
$$\int\limits_{0}^{1} \frac{\left(x^{2} + 2 x\right) - 1}{- 3 x + \left(2 x^{3} + 3 x^{2}\right)}\, dx$$
Integral((x^2 + 2*x - 1)/(2*x^3 + 3*x^2 - 3*x), (x, 0, 1))
Respuesta (Indefinida)
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// / ____ \ \
|| ____ |4*\/ 33 *(3/4 + x)| |
/ ||-\/ 33 *acoth|------------------| |
| || \ 33 / 2 33|
| 2 ||---------------------------------- for (3/4 + x) > --| / 2 \
| x + 2*x - 1 || 132 16| log(x) log\-3 + 2*x + 3*x/
| ----------------- dx = C + 6*|< | + ------ + --------------------
| 3 2 || / ____ \ | 3 12
| 2*x + 3*x - 3*x || ____ |4*\/ 33 *(3/4 + x)| |
| ||-\/ 33 *atanh|------------------| |
/ || \ 33 / 2 33|
||---------------------------------- for (3/4 + x) < --|
\\ 132 16/
$$\int \frac{\left(x^{2} + 2 x\right) - 1}{- 3 x + \left(2 x^{3} + 3 x^{2}\right)}\, dx = C + 6 \left(\begin{cases} - \frac{\sqrt{33} \operatorname{acoth}{\left(\frac{4 \sqrt{33} \left(x + \frac{3}{4}\right)}{33} \right)}}{132} & \text{for}\: \left(x + \frac{3}{4}\right)^{2} > \frac{33}{16} \\- \frac{\sqrt{33} \operatorname{atanh}{\left(\frac{4 \sqrt{33} \left(x + \frac{3}{4}\right)}{33} \right)}}{132} & \text{for}\: \left(x + \frac{3}{4}\right)^{2} < \frac{33}{16} \end{cases}\right) + \frac{\log{\left(x \right)}}{3} + \frac{\log{\left(2 x^{2} + 3 x - 3 \right)}}{12}$$
Gráfica
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.