Sr Examen
Integral de 1/(7sin(x)+9cos(x)+2) dx
Solución
Ha introducido
[src]
1 / | | 1 | ----------------------- dx | 7*sin(x) + 9*cos(x) + 2 | / 0
$$\int\limits_{0}^{1} \frac{1}{\left(7 \sin{\left(x \right)} + 9 \cos{\left(x \right)}\right) + 2}\, dx$$
Integral(1/(7*sin(x) + 9*cos(x) + 2), (x, 0, 1))
Respuesta (Indefinida)
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/ ____ \ / ____ \ / ____ | 3*\/ 14 /x\| ____ | 3*\/ 14 /x\| | \/ 14 *log|-1 - -------- + tan|-|| \/ 14 *log|-1 + -------- + tan|-|| | 1 \ 7 \2// \ 7 \2// | ----------------------- dx = C - ---------------------------------- + ---------------------------------- | 7*sin(x) + 9*cos(x) + 2 42 42 | /
$$\int \frac{1}{\left(7 \sin{\left(x \right)} + 9 \cos{\left(x \right)}\right) + 2}\, dx = C + \frac{\sqrt{14} \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 + \frac{3 \sqrt{14}}{7} \right)}}{42} - \frac{\sqrt{14} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{3 \sqrt{14}}{7} - 1 \right)}}{42}$$
Gráfica
Respuesta
[src]
/ / ____\\ / ____\ / / ____\\ / ____ \
____ | | 3*\/ 14 || ____ | 3*\/ 14 | ____ | | 3*\/ 14 || ____ | 3*\/ 14 |
\/ 14 *|pi*I + log|1 - tan(1/2) + --------|| \/ 14 *log|-1 + --------| \/ 14 *|pi*I + log|1 + --------|| \/ 14 *log|-1 + -------- + tan(1/2)|
\ \ 7 // \ 7 / \ \ 7 // \ 7 /
- -------------------------------------------- - ------------------------- + --------------------------------- + ------------------------------------
42 42 42 42
$$\frac{\sqrt{14} \log{\left(-1 + \tan{\left(\frac{1}{2} \right)} + \frac{3 \sqrt{14}}{7} \right)}}{42} - \frac{\sqrt{14} \log{\left(-1 + \frac{3 \sqrt{14}}{7} \right)}}{42} - \frac{\sqrt{14} \left(\log{\left(- \tan{\left(\frac{1}{2} \right)} + 1 + \frac{3 \sqrt{14}}{7} \right)} + i \pi\right)}{42} + \frac{\sqrt{14} \left(\log{\left(1 + \frac{3 \sqrt{14}}{7} \right)} + i \pi\right)}{42}$$
=
=
/ / ____\\ / ____\ / / ____\\ / ____ \
____ | | 3*\/ 14 || ____ | 3*\/ 14 | ____ | | 3*\/ 14 || ____ | 3*\/ 14 |
\/ 14 *|pi*I + log|1 - tan(1/2) + --------|| \/ 14 *log|-1 + --------| \/ 14 *|pi*I + log|1 + --------|| \/ 14 *log|-1 + -------- + tan(1/2)|
\ \ 7 // \ 7 / \ \ 7 // \ 7 /
- -------------------------------------------- - ------------------------- + --------------------------------- + ------------------------------------
42 42 42 42
$$\frac{\sqrt{14} \log{\left(-1 + \tan{\left(\frac{1}{2} \right)} + \frac{3 \sqrt{14}}{7} \right)}}{42} - \frac{\sqrt{14} \log{\left(-1 + \frac{3 \sqrt{14}}{7} \right)}}{42} - \frac{\sqrt{14} \left(\log{\left(- \tan{\left(\frac{1}{2} \right)} + 1 + \frac{3 \sqrt{14}}{7} \right)} + i \pi\right)}{42} + \frac{\sqrt{14} \left(\log{\left(1 + \frac{3 \sqrt{14}}{7} \right)} + i \pi\right)}{42}$$
-sqrt(14)*(pi*i + log(1 - tan(1/2) + 3*sqrt(14)/7))/42 - sqrt(14)*log(-1 + 3*sqrt(14)/7)/42 + sqrt(14)*(pi*i + log(1 + 3*sqrt(14)/7))/42 + sqrt(14)*log(-1 + 3*sqrt(14)/7 + tan(1/2))/42
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.