Sr Examen
Integral de 1/(2+5cosx) dx
Solución
Ha introducido
[src]
1 / | | 1 | ------------ dx | 2 + 5*cos(x) | / 0
$$\int\limits_{0}^{1} \frac{1}{5 \cos{\left(x \right)} + 2}\, dx$$
Integral(1/(2 + 5*cos(x)), (x, 0, 1))
Respuesta (Indefinida)
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/ ____ \ / ____ \ / ____ | \/ 21 /x\| ____ |\/ 21 /x\| | \/ 21 *log|- ------ + tan|-|| \/ 21 *log|------ + tan|-|| | 1 \ 3 \2// \ 3 \2// | ------------ dx = C - ----------------------------- + --------------------------- | 2 + 5*cos(x) 21 21 | /
$$\int \frac{1}{5 \cos{\left(x \right)} + 2}\, dx = C - \frac{\sqrt{21} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{\sqrt{21}}{3} \right)}}{21} + \frac{\sqrt{21} \log{\left(\tan{\left(\frac{x}{2} \right)} + \frac{\sqrt{21}}{3} \right)}}{21}$$
Gráfica
Respuesta
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/ / ____\\ / ____\ / / ____\\ / ____ \
____ | | \/ 21 || ____ |\/ 21 | ____ | |\/ 21 || ____ |\/ 21 |
\/ 21 *|pi*I + log|-tan(1/2) + ------|| \/ 21 *log|------| \/ 21 *|pi*I + log|------|| \/ 21 *log|------ + tan(1/2)|
\ \ 3 // \ 3 / \ \ 3 // \ 3 /
- --------------------------------------- - ------------------ + --------------------------- + -----------------------------
21 21 21 21
$$- \frac{\sqrt{21} \log{\left(\frac{\sqrt{21}}{3} \right)}}{21} + \frac{\sqrt{21} \log{\left(\tan{\left(\frac{1}{2} \right)} + \frac{\sqrt{21}}{3} \right)}}{21} - \frac{\sqrt{21} \left(\log{\left(- \tan{\left(\frac{1}{2} \right)} + \frac{\sqrt{21}}{3} \right)} + i \pi\right)}{21} + \frac{\sqrt{21} \left(\log{\left(\frac{\sqrt{21}}{3} \right)} + i \pi\right)}{21}$$
=
=
/ / ____\\ / ____\ / / ____\\ / ____ \
____ | | \/ 21 || ____ |\/ 21 | ____ | |\/ 21 || ____ |\/ 21 |
\/ 21 *|pi*I + log|-tan(1/2) + ------|| \/ 21 *log|------| \/ 21 *|pi*I + log|------|| \/ 21 *log|------ + tan(1/2)|
\ \ 3 // \ 3 / \ \ 3 // \ 3 /
- --------------------------------------- - ------------------ + --------------------------- + -----------------------------
21 21 21 21
$$- \frac{\sqrt{21} \log{\left(\frac{\sqrt{21}}{3} \right)}}{21} + \frac{\sqrt{21} \log{\left(\tan{\left(\frac{1}{2} \right)} + \frac{\sqrt{21}}{3} \right)}}{21} - \frac{\sqrt{21} \left(\log{\left(- \tan{\left(\frac{1}{2} \right)} + \frac{\sqrt{21}}{3} \right)} + i \pi\right)}{21} + \frac{\sqrt{21} \left(\log{\left(\frac{\sqrt{21}}{3} \right)} + i \pi\right)}{21}$$
-sqrt(21)*(pi*i + log(-tan(1/2) + sqrt(21)/3))/21 - sqrt(21)*log(sqrt(21)/3)/21 + sqrt(21)*(pi*i + log(sqrt(21)/3))/21 + sqrt(21)*log(sqrt(21)/3 + tan(1/2))/21
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.