Sr Examen
Integral de 1/(-5sinx+3cosx) dx
Solución
Ha introducido
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1 / | | 1 | -------------------- dx | -5*sin(x) + 3*cos(x) | / 0
$$\int\limits_{0}^{1} \frac{1}{- 5 \sin{\left(x \right)} + 3 \cos{\left(x \right)}}\, dx$$
Integral(1/(-5*sin(x) + 3*cos(x)), (x, 0, 1))
Respuesta (Indefinida)
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/ ____ \ / ____ \ / ____ |5 \/ 34 /x\| ____ |5 \/ 34 /x\| | \/ 34 *log|- - ------ + tan|-|| \/ 34 *log|- + ------ + tan|-|| | 1 \3 3 \2// \3 3 \2// | -------------------- dx = C - ------------------------------- + ------------------------------- | -5*sin(x) + 3*cos(x) 34 34 | /
$$\int \frac{1}{- 5 \sin{\left(x \right)} + 3 \cos{\left(x \right)}}\, dx = C + \frac{\sqrt{34} \log{\left(\tan{\left(\frac{x}{2} \right)} + \frac{5}{3} + \frac{\sqrt{34}}{3} \right)}}{34} - \frac{\sqrt{34} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{\sqrt{34}}{3} + \frac{5}{3} \right)}}{34}$$
Gráfica
Respuesta
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/ ____\ / ____ \ / / ____\\ / ____ \
____ |5 \/ 34 | ____ |5 \/ 34 | ____ | | 5 \/ 34 || ____ |5 \/ 34 |
\/ 34 *log|- + ------| \/ 34 *log|- - ------ + tan(1/2)| \/ 34 *|pi*I + log|- - + ------|| \/ 34 *log|- + ------ + tan(1/2)|
\3 3 / \3 3 / \ \ 3 3 // \3 3 /
- ---------------------- - --------------------------------- + --------------------------------- + ---------------------------------
34 34 34 34
$$- \frac{\sqrt{34} \log{\left(\frac{5}{3} + \frac{\sqrt{34}}{3} \right)}}{34} - \frac{\sqrt{34} \log{\left(- \frac{\sqrt{34}}{3} + \tan{\left(\frac{1}{2} \right)} + \frac{5}{3} \right)}}{34} + \frac{\sqrt{34} \log{\left(\tan{\left(\frac{1}{2} \right)} + \frac{5}{3} + \frac{\sqrt{34}}{3} \right)}}{34} + \frac{\sqrt{34} \left(\log{\left(- \frac{5}{3} + \frac{\sqrt{34}}{3} \right)} + i \pi\right)}{34}$$
=
=
/ ____\ / ____ \ / / ____\\ / ____ \
____ |5 \/ 34 | ____ |5 \/ 34 | ____ | | 5 \/ 34 || ____ |5 \/ 34 |
\/ 34 *log|- + ------| \/ 34 *log|- - ------ + tan(1/2)| \/ 34 *|pi*I + log|- - + ------|| \/ 34 *log|- + ------ + tan(1/2)|
\3 3 / \3 3 / \ \ 3 3 // \3 3 /
- ---------------------- - --------------------------------- + --------------------------------- + ---------------------------------
34 34 34 34
$$- \frac{\sqrt{34} \log{\left(\frac{5}{3} + \frac{\sqrt{34}}{3} \right)}}{34} - \frac{\sqrt{34} \log{\left(- \frac{\sqrt{34}}{3} + \tan{\left(\frac{1}{2} \right)} + \frac{5}{3} \right)}}{34} + \frac{\sqrt{34} \log{\left(\tan{\left(\frac{1}{2} \right)} + \frac{5}{3} + \frac{\sqrt{34}}{3} \right)}}{34} + \frac{\sqrt{34} \left(\log{\left(- \frac{5}{3} + \frac{\sqrt{34}}{3} \right)} + i \pi\right)}{34}$$
-sqrt(34)*log(5/3 + sqrt(34)/3)/34 - sqrt(34)*log(5/3 - sqrt(34)/3 + tan(1/2))/34 + sqrt(34)*(pi*i + log(-5/3 + sqrt(34)/3))/34 + sqrt(34)*log(5/3 + sqrt(34)/3 + tan(1/2))/34
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.