Sr Examen
Integral de (dx)/(3*cos(x)-4*sin(x)) dx
Solución
Ha introducido
[src]
1 / | | 1 | ------------------- dx | 3*cos(x) - 4*sin(x) | / 0
$$\int\limits_{0}^{1} \frac{1}{- 4 \sin{\left(x \right)} + 3 \cos{\left(x \right)}}\, dx$$
Integral(1/(3*cos(x) - 4*sin(x)), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ / 1 /x\\ / /x\\ | log|- - + tan|-|| log|3 + tan|-|| | 1 \ 3 \2// \ \2// | ------------------- dx = C - ----------------- + --------------- | 3*cos(x) - 4*sin(x) 5 5 | /
$$\int \frac{1}{- 4 \sin{\left(x \right)} + 3 \cos{\left(x \right)}}\, dx = C - \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{1}{3} \right)}}{5} + \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} + 3 \right)}}{5}$$
Gráfica
Respuesta
[src]
2*log(3) log(-1/3 + tan(1/2)) log(3 + tan(1/2)) pi*I
- -------- - -------------------- + ----------------- + ----
5 5 5 5
$$- \frac{2 \log{\left(3 \right)}}{5} + \frac{\log{\left(\tan{\left(\frac{1}{2} \right)} + 3 \right)}}{5} - \frac{\log{\left(- \frac{1}{3} + \tan{\left(\frac{1}{2} \right)} \right)}}{5} + \frac{i \pi}{5}$$
=
=
2*log(3) log(-1/3 + tan(1/2)) log(3 + tan(1/2)) pi*I
- -------- - -------------------- + ----------------- + ----
5 5 5 5
$$- \frac{2 \log{\left(3 \right)}}{5} + \frac{\log{\left(\tan{\left(\frac{1}{2} \right)} + 3 \right)}}{5} - \frac{\log{\left(- \frac{1}{3} + \tan{\left(\frac{1}{2} \right)} \right)}}{5} + \frac{i \pi}{5}$$
-2*log(3)/5 - log(-1/3 + tan(1/2))/5 + log(3 + tan(1/2))/5 + pi*i/5
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.