Sr Examen
Integral de 1/(7sinx+5cosx) dx
Solución
Ha introducido
[src]
1 / | | 1 | ------------------- dx | 7*sin(x) + 5*cos(x) | / 0
$$\int\limits_{0}^{1} \frac{1}{7 \sin{\left(x \right)} + 5 \cos{\left(x \right)}}\, dx$$
Integral(1/(7*sin(x) + 5*cos(x)), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ ____ \ / ____ \ / ____ | 7 \/ 74 /x\| ____ | 7 \/ 74 /x\| | \/ 74 *log|- - - ------ + tan|-|| \/ 74 *log|- - + ------ + tan|-|| | 1 \ 5 5 \2// \ 5 5 \2// | ------------------- dx = C - --------------------------------- + --------------------------------- | 7*sin(x) + 5*cos(x) 74 74 | /
$$\int \frac{1}{7 \sin{\left(x \right)} + 5 \cos{\left(x \right)}}\, dx = C + \frac{\sqrt{74} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{7}{5} + \frac{\sqrt{74}}{5} \right)}}{74} - \frac{\sqrt{74} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{\sqrt{74}}{5} - \frac{7}{5} \right)}}{74}$$
Gráfica
Respuesta
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/ / ____\\ / ____\ / / ____\\ / ____ \
____ | |7 \/ 74 || ____ | 7 \/ 74 | ____ | |7 \/ 74 || ____ | 7 \/ 74 |
\/ 74 *|pi*I + log|- - tan(1/2) + ------|| \/ 74 *log|- - + ------| \/ 74 *|pi*I + log|- + ------|| \/ 74 *log|- - + ------ + tan(1/2)|
\ \5 5 // \ 5 5 / \ \5 5 // \ 5 5 /
- ------------------------------------------ - ------------------------ + ------------------------------- + -----------------------------------
74 74 74 74
$$\frac{\sqrt{74} \log{\left(- \frac{7}{5} + \tan{\left(\frac{1}{2} \right)} + \frac{\sqrt{74}}{5} \right)}}{74} - \frac{\sqrt{74} \log{\left(- \frac{7}{5} + \frac{\sqrt{74}}{5} \right)}}{74} - \frac{\sqrt{74} \left(\log{\left(- \tan{\left(\frac{1}{2} \right)} + \frac{7}{5} + \frac{\sqrt{74}}{5} \right)} + i \pi\right)}{74} + \frac{\sqrt{74} \left(\log{\left(\frac{7}{5} + \frac{\sqrt{74}}{5} \right)} + i \pi\right)}{74}$$
=
=
/ / ____\\ / ____\ / / ____\\ / ____ \
____ | |7 \/ 74 || ____ | 7 \/ 74 | ____ | |7 \/ 74 || ____ | 7 \/ 74 |
\/ 74 *|pi*I + log|- - tan(1/2) + ------|| \/ 74 *log|- - + ------| \/ 74 *|pi*I + log|- + ------|| \/ 74 *log|- - + ------ + tan(1/2)|
\ \5 5 // \ 5 5 / \ \5 5 // \ 5 5 /
- ------------------------------------------ - ------------------------ + ------------------------------- + -----------------------------------
74 74 74 74
$$\frac{\sqrt{74} \log{\left(- \frac{7}{5} + \tan{\left(\frac{1}{2} \right)} + \frac{\sqrt{74}}{5} \right)}}{74} - \frac{\sqrt{74} \log{\left(- \frac{7}{5} + \frac{\sqrt{74}}{5} \right)}}{74} - \frac{\sqrt{74} \left(\log{\left(- \tan{\left(\frac{1}{2} \right)} + \frac{7}{5} + \frac{\sqrt{74}}{5} \right)} + i \pi\right)}{74} + \frac{\sqrt{74} \left(\log{\left(\frac{7}{5} + \frac{\sqrt{74}}{5} \right)} + i \pi\right)}{74}$$
-sqrt(74)*(pi*i + log(7/5 - tan(1/2) + sqrt(74)/5))/74 - sqrt(74)*log(-7/5 + sqrt(74)/5)/74 + sqrt(74)*(pi*i + log(7/5 + sqrt(74)/5))/74 + sqrt(74)*log(-7/5 + sqrt(74)/5 + tan(1/2))/74
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.