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