Sr Examen
Integral de (4x+3)/(sqrt1+4x-x^2) dx
Solución
Ha introducido
[src]
1 / | | 4*x + 3 | ---------------- dx | ___ 2 | \/ 1 + 4*x - x | / 0
$$\int\limits_{0}^{1} \frac{4 x + 3}{- x^{2} + \left(4 x + \sqrt{1}\right)}\, dx$$
Integral((4*x + 3)/(sqrt(1) + 4*x - x^2), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / ___ \ \
|| ___ |\/ 5 *(-2 + x)| |
||-\/ 5 *acoth|--------------| |
/ || \ 5 / 2 |
| ||----------------------------- for (-2 + x) > 5|
| 4*x + 3 || 5 | / 2 \
| ---------------- dx = C - 11*|< | - 2*log\-1 + x - 4*x/
| ___ 2 || / ___ \ |
| \/ 1 + 4*x - x || ___ |\/ 5 *(-2 + x)| |
| ||-\/ 5 *atanh|--------------| |
/ || \ 5 / 2 |
||----------------------------- for (-2 + x) < 5|
\\ 5 /
$$\int \frac{4 x + 3}{- x^{2} + \left(4 x + \sqrt{1}\right)}\, dx = C - 11 \left(\begin{cases} - \frac{\sqrt{5} \operatorname{acoth}{\left(\frac{\sqrt{5} \left(x - 2\right)}{5} \right)}}{5} & \text{for}\: \left(x - 2\right)^{2} > 5 \\- \frac{\sqrt{5} \operatorname{atanh}{\left(\frac{\sqrt{5} \left(x - 2\right)}{5} \right)}}{5} & \text{for}\: \left(x - 2\right)^{2} < 5 \end{cases}\right) - 2 \log{\left(x^{2} - 4 x - 1 \right)}$$
Gráfica
Respuesta
[src]
/ ___\ / ___\ / ___\ / ___\ | 11*\/ 5 | / ___\ | 11*\/ 5 | / / ___\\ | 11*\/ 5 | / ___\ | 11*\/ 5 | / / ___\\ |2 - --------|*log\-2 + \/ 5 / + |2 + --------|*\pi*I + log\2 + \/ 5 // - |2 - --------|*log\-1 + \/ 5 / - |2 + --------|*\pi*I + log\1 + \/ 5 // \ 10 / \ 10 / \ 10 / \ 10 /
$$- \left(2 - \frac{11 \sqrt{5}}{10}\right) \log{\left(-1 + \sqrt{5} \right)} + \left(2 - \frac{11 \sqrt{5}}{10}\right) \log{\left(-2 + \sqrt{5} \right)} - \left(2 + \frac{11 \sqrt{5}}{10}\right) \left(\log{\left(1 + \sqrt{5} \right)} + i \pi\right) + \left(2 + \frac{11 \sqrt{5}}{10}\right) \left(\log{\left(2 + \sqrt{5} \right)} + i \pi\right)$$
=
=
/ ___\ / ___\ / ___\ / ___\ | 11*\/ 5 | / ___\ | 11*\/ 5 | / / ___\\ | 11*\/ 5 | / ___\ | 11*\/ 5 | / / ___\\ |2 - --------|*log\-2 + \/ 5 / + |2 + --------|*\pi*I + log\2 + \/ 5 // - |2 - --------|*log\-1 + \/ 5 / - |2 + --------|*\pi*I + log\1 + \/ 5 // \ 10 / \ 10 / \ 10 / \ 10 /
$$- \left(2 - \frac{11 \sqrt{5}}{10}\right) \log{\left(-1 + \sqrt{5} \right)} + \left(2 - \frac{11 \sqrt{5}}{10}\right) \log{\left(-2 + \sqrt{5} \right)} - \left(2 + \frac{11 \sqrt{5}}{10}\right) \left(\log{\left(1 + \sqrt{5} \right)} + i \pi\right) + \left(2 + \frac{11 \sqrt{5}}{10}\right) \left(\log{\left(2 + \sqrt{5} \right)} + i \pi\right)$$
(2 - 11*sqrt(5)/10)*log(-2 + sqrt(5)) + (2 + 11*sqrt(5)/10)*(pi*i + log(2 + sqrt(5))) - (2 - 11*sqrt(5)/10)*log(-1 + sqrt(5)) - (2 + 11*sqrt(5)/10)*(pi*i + log(1 + sqrt(5)))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.