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