Sr Examen
Integral de (1)/(1+5cosx) dx
Solución
Ha introducido
[src]
1 / | | 1 | ------------ dx | 1 + 5*cos(x) | / 0
$$\int\limits_{0}^{1} \frac{1}{5 \cos{\left(x \right)} + 1}\, dx$$
Integral(1/(1 + 5*cos(x)), (x, 0, 1))
Respuesta (Indefinida)
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/ ___ \ / ___ \ / ___ | \/ 6 /x\| ___ |\/ 6 /x\| | \/ 6 *log|- ----- + tan|-|| \/ 6 *log|----- + tan|-|| | 1 \ 2 \2// \ 2 \2// | ------------ dx = C - --------------------------- + ------------------------- | 1 + 5*cos(x) 12 12 | /
$$\int \frac{1}{5 \cos{\left(x \right)} + 1}\, dx = C - \frac{\sqrt{6} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{\sqrt{6}}{2} \right)}}{12} + \frac{\sqrt{6} \log{\left(\tan{\left(\frac{x}{2} \right)} + \frac{\sqrt{6}}{2} \right)}}{12}$$
Gráfica
Respuesta
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/ / ___ \\ / ___\ / / ___\\ / ___ \
___ | |\/ 6 || ___ |\/ 6 | ___ | |\/ 6 || ___ |\/ 6 |
\/ 6 *|pi*I + log|----- - tan(1/2)|| \/ 6 *log|-----| \/ 6 *|pi*I + log|-----|| \/ 6 *log|----- + tan(1/2)|
\ \ 2 // \ 2 / \ \ 2 // \ 2 /
- ------------------------------------ - ---------------- + ------------------------- + ---------------------------
12 12 12 12
$$- \frac{\sqrt{6} \log{\left(\frac{\sqrt{6}}{2} \right)}}{12} + \frac{\sqrt{6} \log{\left(\tan{\left(\frac{1}{2} \right)} + \frac{\sqrt{6}}{2} \right)}}{12} - \frac{\sqrt{6} \left(\log{\left(- \tan{\left(\frac{1}{2} \right)} + \frac{\sqrt{6}}{2} \right)} + i \pi\right)}{12} + \frac{\sqrt{6} \left(\log{\left(\frac{\sqrt{6}}{2} \right)} + i \pi\right)}{12}$$
=
=
/ / ___ \\ / ___\ / / ___\\ / ___ \
___ | |\/ 6 || ___ |\/ 6 | ___ | |\/ 6 || ___ |\/ 6 |
\/ 6 *|pi*I + log|----- - tan(1/2)|| \/ 6 *log|-----| \/ 6 *|pi*I + log|-----|| \/ 6 *log|----- + tan(1/2)|
\ \ 2 // \ 2 / \ \ 2 // \ 2 /
- ------------------------------------ - ---------------- + ------------------------- + ---------------------------
12 12 12 12
$$- \frac{\sqrt{6} \log{\left(\frac{\sqrt{6}}{2} \right)}}{12} + \frac{\sqrt{6} \log{\left(\tan{\left(\frac{1}{2} \right)} + \frac{\sqrt{6}}{2} \right)}}{12} - \frac{\sqrt{6} \left(\log{\left(- \tan{\left(\frac{1}{2} \right)} + \frac{\sqrt{6}}{2} \right)} + i \pi\right)}{12} + \frac{\sqrt{6} \left(\log{\left(\frac{\sqrt{6}}{2} \right)} + i \pi\right)}{12}$$
-sqrt(6)*(pi*i + log(sqrt(6)/2 - tan(1/2)))/12 - sqrt(6)*log(sqrt(6)/2)/12 + sqrt(6)*(pi*i + log(sqrt(6)/2))/12 + sqrt(6)*log(sqrt(6)/2 + tan(1/2))/12
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.