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