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