Sr Examen
Integral de 1/(2sinx+9cosx+11) dx
Solución
Ha introducido
[src]
1 / | | 1 | ------------------------ dx | 2*sin(x) + 9*cos(x) + 11 | / 0
$$\int\limits_{0}^{1} \frac{1}{\left(2 \sin{\left(x \right)} + 9 \cos{\left(x \right)}\right) + 11}\, dx$$
Integral(1/(2*sin(x) + 9*cos(x) + 11), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ /x\\ /x pi\
| tan|-|| |- - --|
/ |1 \2/| |2 2 |
| atan|- + ------| pi*floor|------|
| 1 \3 3 / \ pi /
| ------------------------ dx = C + ---------------- + ----------------
| 2*sin(x) + 9*cos(x) + 11 3 3
|
/
$$\int \frac{1}{\left(2 \sin{\left(x \right)} + 9 \cos{\left(x \right)}\right) + 11}\, dx = C + \frac{\operatorname{atan}{\left(\frac{\tan{\left(\frac{x}{2} \right)}}{3} + \frac{1}{3} \right)}}{3} + \frac{\pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor}{3}$$
Gráfica
Respuesta
[src]
/1 tan(1/2)\
atan|- + --------|
atan(1/3) \3 3 /
- --------- + ------------------
3 3
$$- \frac{\operatorname{atan}{\left(\frac{1}{3} \right)}}{3} + \frac{\operatorname{atan}{\left(\frac{\tan{\left(\frac{1}{2} \right)}}{3} + \frac{1}{3} \right)}}{3}$$
=
=
/1 tan(1/2)\
atan|- + --------|
atan(1/3) \3 3 /
- --------- + ------------------
3 3
$$- \frac{\operatorname{atan}{\left(\frac{1}{3} \right)}}{3} + \frac{\operatorname{atan}{\left(\frac{\tan{\left(\frac{1}{2} \right)}}{3} + \frac{1}{3} \right)}}{3}$$
-atan(1/3)/3 + atan(1/3 + tan(1/2)/3)/3
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.