Sr Examen
Integral de sin(x)/(5+3sin(x)) dx
Solución
Ha introducido
[src]
1 / | | sin(x) | ------------ dx | 5 + 3*sin(x) | / 0
$$\int\limits_{0}^{1} \frac{\sin{\left(x \right)}}{3 \sin{\left(x \right)} + 5}\, dx$$
Integral(sin(x)/(5 + 3*sin(x)), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ /x\\ /x pi\
| 5*tan|-|| |- - --|
/ |3 \2/| |2 2 |
| 5*atan|- + --------| 5*pi*floor|------|
| sin(x) \4 4 / x \ pi /
| ------------ dx = C - -------------------- + - - ------------------
| 5 + 3*sin(x) 6 3 6
|
/
$$\int \frac{\sin{\left(x \right)}}{3 \sin{\left(x \right)} + 5}\, dx = C + \frac{x}{3} - \frac{5 \operatorname{atan}{\left(\frac{5 \tan{\left(\frac{x}{2} \right)}}{4} + \frac{3}{4} \right)}}{6} - \frac{5 \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor}{6}$$
Gráfica
Respuesta
[src]
/3 5*tan(1/2)\
5*atan|- + ----------|
1 \4 4 / 5*atan(3/4)
- - ---------------------- + -----------
3 6 6
$$- \frac{5 \operatorname{atan}{\left(\frac{5 \tan{\left(\frac{1}{2} \right)}}{4} + \frac{3}{4} \right)}}{6} + \frac{1}{3} + \frac{5 \operatorname{atan}{\left(\frac{3}{4} \right)}}{6}$$
=
=
/3 5*tan(1/2)\
5*atan|- + ----------|
1 \4 4 / 5*atan(3/4)
- - ---------------------- + -----------
3 6 6
$$- \frac{5 \operatorname{atan}{\left(\frac{5 \tan{\left(\frac{1}{2} \right)}}{4} + \frac{3}{4} \right)}}{6} + \frac{1}{3} + \frac{5 \operatorname{atan}{\left(\frac{3}{4} \right)}}{6}$$
1/3 - 5*atan(3/4 + 5*tan(1/2)/4)/6 + 5*atan(3/4)/6
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.