Sr Examen
Integral de 1/(5+2sinx+3cosx) dx
Solución
Ha introducido
[src]
1 / | | 1 | ----------------------- dx | 5 + 2*sin(x) + 3*cos(x) | / 0
$$\int\limits_{0}^{1} \frac{1}{\left(2 \sin{\left(x \right)} + 5\right) + 3 \cos{\left(x \right)}}\, dx$$
Integral(1/(5 + 2*sin(x) + 3*cos(x)), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ /x pi\ / ___ /x\\\
| |- - --| | ___ \/ 3 *tan|-|||
/ ___ | |2 2 | |\/ 3 \2/||
| \/ 3 *|pi*floor|------| + atan|----- + ------------||
| 1 \ \ pi / \ 3 3 //
| ----------------------- dx = C + -----------------------------------------------------
| 5 + 2*sin(x) + 3*cos(x) 3
|
/
$$\int \frac{1}{\left(2 \sin{\left(x \right)} + 5\right) + 3 \cos{\left(x \right)}}\, dx = C + \frac{\sqrt{3} \left(\operatorname{atan}{\left(\frac{\sqrt{3} \tan{\left(\frac{x}{2} \right)}}{3} + \frac{\sqrt{3}}{3} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{3}$$
Gráfica
Respuesta
[src]
/ / ___ ___ \\
___ | |\/ 3 \/ 3 *tan(1/2)||
\/ 3 *|-pi + atan|----- + --------------|| ___
\ \ 3 3 // 5*pi*\/ 3
------------------------------------------ + ----------
3 18
$$\frac{\sqrt{3} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{3} \tan{\left(\frac{1}{2} \right)}}{3} + \frac{\sqrt{3}}{3} \right)}\right)}{3} + \frac{5 \sqrt{3} \pi}{18}$$
=
=
/ / ___ ___ \\
___ | |\/ 3 \/ 3 *tan(1/2)||
\/ 3 *|-pi + atan|----- + --------------|| ___
\ \ 3 3 // 5*pi*\/ 3
------------------------------------------ + ----------
3 18
$$\frac{\sqrt{3} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{3} \tan{\left(\frac{1}{2} \right)}}{3} + \frac{\sqrt{3}}{3} \right)}\right)}{3} + \frac{5 \sqrt{3} \pi}{18}$$
sqrt(3)*(-pi + atan(sqrt(3)/3 + sqrt(3)*tan(1/2)/3))/3 + 5*pi*sqrt(3)/18
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.