Sr Examen
Integral de (sinx)/(5+4sinx) dx
Solución
Ha introducido
[src]
pi -- 2 / | | sin(x) | ------------ dx | 5 + 4*sin(x) | / 0
$$\int\limits_{0}^{\frac{\pi}{2}} \frac{\sin{\left(x \right)}}{4 \sin{\left(x \right)} + 5}\, dx$$
Integral(sin(x)/(5 + 4*sin(x)), (x, 0, pi/2))
Respuesta (Indefinida)
[src]
/ /x\\ /x pi\
| 5*tan|-|| |- - --|
/ |4 \2/| |2 2 |
| 5*atan|- + --------| 5*pi*floor|------|
| sin(x) \3 3 / x \ pi /
| ------------ dx = C - -------------------- + - - ------------------
| 5 + 4*sin(x) 6 4 6
|
/
$$\int \frac{\sin{\left(x \right)}}{4 \sin{\left(x \right)} + 5}\, dx = C + \frac{x}{4} - \frac{5 \operatorname{atan}{\left(\frac{5 \tan{\left(\frac{x}{2} \right)}}{3} + \frac{4}{3} \right)}}{6} - \frac{5 \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor}{6}$$
Gráfica
Respuesta
[src]
5*atan(3) pi 5*atan(4/3)
- --------- + -- + -----------
6 8 6
$$- \frac{5 \operatorname{atan}{\left(3 \right)}}{6} + \frac{\pi}{8} + \frac{5 \operatorname{atan}{\left(\frac{4}{3} \right)}}{6}$$
=
=
5*atan(3) pi 5*atan(4/3)
- --------- + -- + -----------
6 8 6
$$- \frac{5 \operatorname{atan}{\left(3 \right)}}{6} + \frac{\pi}{8} + \frac{5 \operatorname{atan}{\left(\frac{4}{3} \right)}}{6}$$
-5*atan(3)/6 + pi/8 + 5*atan(4/3)/6
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.