Sr Examen
Integral de 1/(3cosx-7sinx) dx
Solución
Ha introducido
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1 / | | 1 | ------------------- dx | 3*cos(x) - 7*sin(x) | / 0
$$\int\limits_{0}^{1} \frac{1}{- 7 \sin{\left(x \right)} + 3 \cos{\left(x \right)}}\, dx$$
Integral(1/(3*cos(x) - 7*sin(x)), (x, 0, 1))
Respuesta (Indefinida)
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/ ____ \ / ____ \ / ____ |7 \/ 58 /x\| ____ |7 \/ 58 /x\| | \/ 58 *log|- - ------ + tan|-|| \/ 58 *log|- + ------ + tan|-|| | 1 \3 3 \2// \3 3 \2// | ------------------- dx = C - ------------------------------- + ------------------------------- | 3*cos(x) - 7*sin(x) 58 58 | /
$$\int \frac{1}{- 7 \sin{\left(x \right)} + 3 \cos{\left(x \right)}}\, dx = C + \frac{\sqrt{58} \log{\left(\tan{\left(\frac{x}{2} \right)} + \frac{7}{3} + \frac{\sqrt{58}}{3} \right)}}{58} - \frac{\sqrt{58} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{\sqrt{58}}{3} + \frac{7}{3} \right)}}{58}$$
Gráfica
Respuesta
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/ ____\ / ____ \ / / ____\\ / ____ \
____ |7 \/ 58 | ____ |7 \/ 58 | ____ | | 7 \/ 58 || ____ |7 \/ 58 |
\/ 58 *log|- + ------| \/ 58 *log|- - ------ + tan(1/2)| \/ 58 *|pi*I + log|- - + ------|| \/ 58 *log|- + ------ + tan(1/2)|
\3 3 / \3 3 / \ \ 3 3 // \3 3 /
- ---------------------- - --------------------------------- + --------------------------------- + ---------------------------------
58 58 58 58
$$- \frac{\sqrt{58} \log{\left(\frac{7}{3} + \frac{\sqrt{58}}{3} \right)}}{58} - \frac{\sqrt{58} \log{\left(- \frac{\sqrt{58}}{3} + \tan{\left(\frac{1}{2} \right)} + \frac{7}{3} \right)}}{58} + \frac{\sqrt{58} \log{\left(\tan{\left(\frac{1}{2} \right)} + \frac{7}{3} + \frac{\sqrt{58}}{3} \right)}}{58} + \frac{\sqrt{58} \left(\log{\left(- \frac{7}{3} + \frac{\sqrt{58}}{3} \right)} + i \pi\right)}{58}$$
=
=
/ ____\ / ____ \ / / ____\\ / ____ \
____ |7 \/ 58 | ____ |7 \/ 58 | ____ | | 7 \/ 58 || ____ |7 \/ 58 |
\/ 58 *log|- + ------| \/ 58 *log|- - ------ + tan(1/2)| \/ 58 *|pi*I + log|- - + ------|| \/ 58 *log|- + ------ + tan(1/2)|
\3 3 / \3 3 / \ \ 3 3 // \3 3 /
- ---------------------- - --------------------------------- + --------------------------------- + ---------------------------------
58 58 58 58
$$- \frac{\sqrt{58} \log{\left(\frac{7}{3} + \frac{\sqrt{58}}{3} \right)}}{58} - \frac{\sqrt{58} \log{\left(- \frac{\sqrt{58}}{3} + \tan{\left(\frac{1}{2} \right)} + \frac{7}{3} \right)}}{58} + \frac{\sqrt{58} \log{\left(\tan{\left(\frac{1}{2} \right)} + \frac{7}{3} + \frac{\sqrt{58}}{3} \right)}}{58} + \frac{\sqrt{58} \left(\log{\left(- \frac{7}{3} + \frac{\sqrt{58}}{3} \right)} + i \pi\right)}{58}$$
-sqrt(58)*log(7/3 + sqrt(58)/3)/58 - sqrt(58)*log(7/3 - sqrt(58)/3 + tan(1/2))/58 + sqrt(58)*(pi*i + log(-7/3 + sqrt(58)/3))/58 + sqrt(58)*log(7/3 + sqrt(58)/3 + tan(1/2))/58
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.