Sr Examen
Integral de 1/(2-3sinx+cos) dx
Solución
Ha introducido
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0 / | | 1 | --------------------- dx | 2 - 3*sin(x) + cos(x) | / -157 ----- 100
$$\int\limits_{- \frac{157}{100}}^{0} \frac{1}{\left(2 - 3 \sin{\left(x \right)}\right) + \cos{\left(x \right)}}\, dx$$
Integral(1/(2 - 3*sin(x) + cos(x)), (x, -157/100, 0))
Respuesta (Indefinida)
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/ ___ / ___ /x\\ ___ / ___ /x\\ | \/ 6 *log|-3 + \/ 6 + tan|-|| \/ 6 *log|-3 - \/ 6 + tan|-|| | 1 \ \2// \ \2// | --------------------- dx = C - ------------------------------ + ------------------------------ | 2 - 3*sin(x) + cos(x) 6 6 | /
$$\int \frac{1}{\left(2 - 3 \sin{\left(x \right)}\right) + \cos{\left(x \right)}}\, dx = C + \frac{\sqrt{6} \log{\left(\tan{\left(\frac{x}{2} \right)} - 3 - \sqrt{6} \right)}}{6} - \frac{\sqrt{6} \log{\left(\tan{\left(\frac{x}{2} \right)} - 3 + \sqrt{6} \right)}}{6}$$
Gráfica
Respuesta
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___ / / ___ /157\\\ ___ / / ___ /157\\\
___ / / ___\\ \/ 6 *|pi*I + log|3 + \/ 6 + tan|---||| ___ / / ___\\ \/ 6 *|pi*I + log|3 - \/ 6 + tan|---|||
\/ 6 *\pi*I + log\3 - \/ 6 // \ \ \200/// \/ 6 *\pi*I + log\3 + \/ 6 // \ \ \200///
- ----------------------------- - ---------------------------------------- + ----------------------------- + ----------------------------------------
6 6 6 6
$$- \frac{\sqrt{6} \left(\log{\left(\tan{\left(\frac{157}{200} \right)} + \sqrt{6} + 3 \right)} + i \pi\right)}{6} - \frac{\sqrt{6} \left(\log{\left(3 - \sqrt{6} \right)} + i \pi\right)}{6} + \frac{\sqrt{6} \left(\log{\left(- \sqrt{6} + \tan{\left(\frac{157}{200} \right)} + 3 \right)} + i \pi\right)}{6} + \frac{\sqrt{6} \left(\log{\left(\sqrt{6} + 3 \right)} + i \pi\right)}{6}$$
=
=
___ / / ___ /157\\\ ___ / / ___ /157\\\
___ / / ___\\ \/ 6 *|pi*I + log|3 + \/ 6 + tan|---||| ___ / / ___\\ \/ 6 *|pi*I + log|3 - \/ 6 + tan|---|||
\/ 6 *\pi*I + log\3 - \/ 6 // \ \ \200/// \/ 6 *\pi*I + log\3 + \/ 6 // \ \ \200///
- ----------------------------- - ---------------------------------------- + ----------------------------- + ----------------------------------------
6 6 6 6
$$- \frac{\sqrt{6} \left(\log{\left(\tan{\left(\frac{157}{200} \right)} + \sqrt{6} + 3 \right)} + i \pi\right)}{6} - \frac{\sqrt{6} \left(\log{\left(3 - \sqrt{6} \right)} + i \pi\right)}{6} + \frac{\sqrt{6} \left(\log{\left(- \sqrt{6} + \tan{\left(\frac{157}{200} \right)} + 3 \right)} + i \pi\right)}{6} + \frac{\sqrt{6} \left(\log{\left(\sqrt{6} + 3 \right)} + i \pi\right)}{6}$$
-sqrt(6)*(pi*i + log(3 - sqrt(6)))/6 - sqrt(6)*(pi*i + log(3 + sqrt(6) + tan(157/200)))/6 + sqrt(6)*(pi*i + log(3 + sqrt(6)))/6 + sqrt(6)*(pi*i + log(3 - sqrt(6) + tan(157/200)))/6
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.