Sr Examen
Integral de (3x-5)/(2x^2-12x+15) dx
Solución
Ha introducido
[src]
1 / | | 3*x - 5 | ---------------- dx | 2 | 2*x - 12*x + 15 | / 0
$$\int\limits_{0}^{1} \frac{3 x - 5}{\left(2 x^{2} - 12 x\right) + 15}\, dx$$
Integral((3*x - 5)/(2*x^2 - 12*x + 15), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / ___ \ \
|| ___ |\/ 6 *(-3 + x)| |
||-\/ 6 *acoth|--------------| |
/ || \ 3 / 2 |
| ||----------------------------- for (-3 + x) > 3/2| / 2\
| 3*x - 5 || 6 | 3*log\15 - 12*x + 2*x /
| ---------------- dx = C + 4*|< | + -----------------------
| 2 || / ___ \ | 4
| 2*x - 12*x + 15 || ___ |\/ 6 *(-3 + x)| |
| ||-\/ 6 *atanh|--------------| |
/ || \ 3 / 2 |
||----------------------------- for (-3 + x) < 3/2|
\\ 6 /
$$\int \frac{3 x - 5}{\left(2 x^{2} - 12 x\right) + 15}\, dx = C + 4 \left(\begin{cases} - \frac{\sqrt{6} \operatorname{acoth}{\left(\frac{\sqrt{6} \left(x - 3\right)}{3} \right)}}{6} & \text{for}\: \left(x - 3\right)^{2} > \frac{3}{2} \\- \frac{\sqrt{6} \operatorname{atanh}{\left(\frac{\sqrt{6} \left(x - 3\right)}{3} \right)}}{6} & \text{for}\: \left(x - 3\right)^{2} < \frac{3}{2} \end{cases}\right) + \frac{3 \log{\left(2 x^{2} - 12 x + 15 \right)}}{4}$$
Gráfica
Respuesta
[src]
/ ___\ / / ___\\ / ___\ / / ___\\ / ___\ / / ___\\ / ___\ / / ___\\ |3 \/ 6 | | | \/ 6 || |3 \/ 6 | | | \/ 6 || |3 \/ 6 | | | \/ 6 || |3 \/ 6 | | | \/ 6 || |- - -----|*|pi*I + log|2 - -----|| + |- + -----|*|pi*I + log|2 + -----|| - |- - -----|*|pi*I + log|3 - -----|| - |- + -----|*|pi*I + log|3 + -----|| \4 3 / \ \ 2 // \4 3 / \ \ 2 // \4 3 / \ \ 2 // \4 3 / \ \ 2 //
$$- \left(\frac{3}{4} + \frac{\sqrt{6}}{3}\right) \left(\log{\left(\frac{\sqrt{6}}{2} + 3 \right)} + i \pi\right) + \left(\frac{3}{4} - \frac{\sqrt{6}}{3}\right) \left(\log{\left(2 - \frac{\sqrt{6}}{2} \right)} + i \pi\right) - \left(\frac{3}{4} - \frac{\sqrt{6}}{3}\right) \left(\log{\left(3 - \frac{\sqrt{6}}{2} \right)} + i \pi\right) + \left(\frac{3}{4} + \frac{\sqrt{6}}{3}\right) \left(\log{\left(\frac{\sqrt{6}}{2} + 2 \right)} + i \pi\right)$$
=
=
/ ___\ / / ___\\ / ___\ / / ___\\ / ___\ / / ___\\ / ___\ / / ___\\ |3 \/ 6 | | | \/ 6 || |3 \/ 6 | | | \/ 6 || |3 \/ 6 | | | \/ 6 || |3 \/ 6 | | | \/ 6 || |- - -----|*|pi*I + log|2 - -----|| + |- + -----|*|pi*I + log|2 + -----|| - |- - -----|*|pi*I + log|3 - -----|| - |- + -----|*|pi*I + log|3 + -----|| \4 3 / \ \ 2 // \4 3 / \ \ 2 // \4 3 / \ \ 2 // \4 3 / \ \ 2 //
$$- \left(\frac{3}{4} + \frac{\sqrt{6}}{3}\right) \left(\log{\left(\frac{\sqrt{6}}{2} + 3 \right)} + i \pi\right) + \left(\frac{3}{4} - \frac{\sqrt{6}}{3}\right) \left(\log{\left(2 - \frac{\sqrt{6}}{2} \right)} + i \pi\right) - \left(\frac{3}{4} - \frac{\sqrt{6}}{3}\right) \left(\log{\left(3 - \frac{\sqrt{6}}{2} \right)} + i \pi\right) + \left(\frac{3}{4} + \frac{\sqrt{6}}{3}\right) \left(\log{\left(\frac{\sqrt{6}}{2} + 2 \right)} + i \pi\right)$$
(3/4 - sqrt(6)/3)*(pi*i + log(2 - sqrt(6)/2)) + (3/4 + sqrt(6)/3)*(pi*i + log(2 + sqrt(6)/2)) - (3/4 - sqrt(6)/3)*(pi*i + log(3 - sqrt(6)/2)) - (3/4 + sqrt(6)/3)*(pi*i + log(3 + sqrt(6)/2))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.