Sr Examen
Integral de 1/(49-48cosx^2) dx
Solución
Ha introducido
[src]
1 / | | 1 | --------------- dx | 2 | 49 - 48*cos (x) | / 0
$$\int\limits_{0}^{1} \frac{1}{49 - 48 \cos^{2}{\left(x \right)}}\, dx$$
Integral(1/(49 - 48*cos(x)^2), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ /x pi\ / /x\ \\ / /x pi\ / /x\ \\ / /x pi\ / /x\ \\ / /x pi\ / /x\ \\
| |- - --| | tan|-| || | |- - --| | tan|-| || _______________ _______________ | |- - --| | tan|-| || _______________ _______________ | |- - --| | tan|-| ||
| |2 2 | | \2/ || ___ | |2 2 | | \2/ || / ___ / ___ | |2 2 | | \2/ || ___ / ___ / ___ | |2 2 | | \2/ ||
97*|pi*floor|------| + atan|------------------|| 56*\/ 3 *|pi*floor|------| + atan|------------------|| 97*\/ 97 - 56*\/ 3 *\/ 97 + 56*\/ 3 *|pi*floor|------| + atan|------------------|| 56*\/ 3 *\/ 97 - 56*\/ 3 *\/ 97 + 56*\/ 3 *|pi*floor|------| + atan|------------------||
/ | \ pi / | _______________|| | \ pi / | _______________|| | \ pi / | _______________|| | \ pi / | _______________||
| | | / ___ || | | / ___ || | | / ___ || | | / ___ ||
| 1 \ \\/ 97 - 56*\/ 3 // \ \\/ 97 - 56*\/ 3 // \ \\/ 97 + 56*\/ 3 // \ \\/ 97 + 56*\/ 3 //
| --------------- dx = C + ------------------------------------------------------- + ------------------------------------------------------- + -------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------
| 2 _______________ _______________ _______________ _______________ _______________ _______________ _______________ _______________
| 49 - 48*cos (x) / ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___
| 9457*\/ 97 - 56*\/ 3 + 5460*\/ 3 *\/ 97 - 56*\/ 3 9457*\/ 97 - 56*\/ 3 + 5460*\/ 3 *\/ 97 - 56*\/ 3 9457*\/ 97 - 56*\/ 3 + 5460*\/ 3 *\/ 97 - 56*\/ 3 9457*\/ 97 - 56*\/ 3 + 5460*\/ 3 *\/ 97 - 56*\/ 3
/
$$\int \frac{1}{49 - 48 \cos^{2}{\left(x \right)}}\, dx = C + \frac{56 \sqrt{3} \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{x}{2} \right)}}{\sqrt{97 - 56 \sqrt{3}}} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{5460 \sqrt{3} \sqrt{97 - 56 \sqrt{3}} + 9457 \sqrt{97 - 56 \sqrt{3}}} + \frac{97 \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{x}{2} \right)}}{\sqrt{97 - 56 \sqrt{3}}} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{5460 \sqrt{3} \sqrt{97 - 56 \sqrt{3}} + 9457 \sqrt{97 - 56 \sqrt{3}}} + \frac{56 \sqrt{3} \sqrt{97 - 56 \sqrt{3}} \sqrt{56 \sqrt{3} + 97} \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{x}{2} \right)}}{\sqrt{56 \sqrt{3} + 97}} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{5460 \sqrt{3} \sqrt{97 - 56 \sqrt{3}} + 9457 \sqrt{97 - 56 \sqrt{3}}} + \frac{97 \sqrt{97 - 56 \sqrt{3}} \sqrt{56 \sqrt{3} + 97} \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{x}{2} \right)}}{\sqrt{56 \sqrt{3} + 97}} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{5460 \sqrt{3} \sqrt{97 - 56 \sqrt{3}} + 9457 \sqrt{97 - 56 \sqrt{3}}}$$
Gráfica
Respuesta
[src]
_______________ _______________
/ tan(1/2) \ / ___ / ___ / / tan(1/2) \\
-pi + atan|------------------| \/ 97 - 56*\/ 3 *\/ 97 + 56*\/ 3 *|-pi + atan|------------------||
| _______________| _______________ _______________ | | _______________||
| / ___ | / ___ / ___ | | / ___ ||
pi \\/ 97 - 56*\/ 3 / pi*\/ 97 - 56*\/ 3 *\/ 97 + 56*\/ 3 \ \\/ 97 + 56*\/ 3 //
--------------------------------------------------- + --------------------------------------------------- + --------------------------------------------------- + ----------------------------------------------------------------------
_______________ _______________ _______________ _______________ _______________ _______________ _______________ _______________
/ ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___
49*\/ 97 - 56*\/ 3 + 28*\/ 3 *\/ 97 - 56*\/ 3 49*\/ 97 - 56*\/ 3 + 28*\/ 3 *\/ 97 - 56*\/ 3 49*\/ 97 - 56*\/ 3 + 28*\/ 3 *\/ 97 - 56*\/ 3 49*\/ 97 - 56*\/ 3 + 28*\/ 3 *\/ 97 - 56*\/ 3
$$\frac{\sqrt{97 - 56 \sqrt{3}} \sqrt{56 \sqrt{3} + 97} \left(- \pi + \operatorname{atan}{\left(\frac{\tan{\left(\frac{1}{2} \right)}}{\sqrt{56 \sqrt{3} + 97}} \right)}\right)}{28 \sqrt{3} \sqrt{97 - 56 \sqrt{3}} + 49 \sqrt{97 - 56 \sqrt{3}}} + \frac{- \pi + \operatorname{atan}{\left(\frac{\tan{\left(\frac{1}{2} \right)}}{\sqrt{97 - 56 \sqrt{3}}} \right)}}{28 \sqrt{3} \sqrt{97 - 56 \sqrt{3}} + 49 \sqrt{97 - 56 \sqrt{3}}} + \frac{\pi}{28 \sqrt{3} \sqrt{97 - 56 \sqrt{3}} + 49 \sqrt{97 - 56 \sqrt{3}}} + \frac{\pi \sqrt{97 - 56 \sqrt{3}} \sqrt{56 \sqrt{3} + 97}}{28 \sqrt{3} \sqrt{97 - 56 \sqrt{3}} + 49 \sqrt{97 - 56 \sqrt{3}}}$$
=
=
_______________ _______________
/ tan(1/2) \ / ___ / ___ / / tan(1/2) \\
-pi + atan|------------------| \/ 97 - 56*\/ 3 *\/ 97 + 56*\/ 3 *|-pi + atan|------------------||
| _______________| _______________ _______________ | | _______________||
| / ___ | / ___ / ___ | | / ___ ||
pi \\/ 97 - 56*\/ 3 / pi*\/ 97 - 56*\/ 3 *\/ 97 + 56*\/ 3 \ \\/ 97 + 56*\/ 3 //
--------------------------------------------------- + --------------------------------------------------- + --------------------------------------------------- + ----------------------------------------------------------------------
_______________ _______________ _______________ _______________ _______________ _______________ _______________ _______________
/ ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___
49*\/ 97 - 56*\/ 3 + 28*\/ 3 *\/ 97 - 56*\/ 3 49*\/ 97 - 56*\/ 3 + 28*\/ 3 *\/ 97 - 56*\/ 3 49*\/ 97 - 56*\/ 3 + 28*\/ 3 *\/ 97 - 56*\/ 3 49*\/ 97 - 56*\/ 3 + 28*\/ 3 *\/ 97 - 56*\/ 3
$$\frac{\sqrt{97 - 56 \sqrt{3}} \sqrt{56 \sqrt{3} + 97} \left(- \pi + \operatorname{atan}{\left(\frac{\tan{\left(\frac{1}{2} \right)}}{\sqrt{56 \sqrt{3} + 97}} \right)}\right)}{28 \sqrt{3} \sqrt{97 - 56 \sqrt{3}} + 49 \sqrt{97 - 56 \sqrt{3}}} + \frac{- \pi + \operatorname{atan}{\left(\frac{\tan{\left(\frac{1}{2} \right)}}{\sqrt{97 - 56 \sqrt{3}}} \right)}}{28 \sqrt{3} \sqrt{97 - 56 \sqrt{3}} + 49 \sqrt{97 - 56 \sqrt{3}}} + \frac{\pi}{28 \sqrt{3} \sqrt{97 - 56 \sqrt{3}} + 49 \sqrt{97 - 56 \sqrt{3}}} + \frac{\pi \sqrt{97 - 56 \sqrt{3}} \sqrt{56 \sqrt{3} + 97}}{28 \sqrt{3} \sqrt{97 - 56 \sqrt{3}} + 49 \sqrt{97 - 56 \sqrt{3}}}$$
pi/(49*sqrt(97 - 56*sqrt(3)) + 28*sqrt(3)*sqrt(97 - 56*sqrt(3))) + (-pi + atan(tan(1/2)/sqrt(97 - 56*sqrt(3))))/(49*sqrt(97 - 56*sqrt(3)) + 28*sqrt(3)*sqrt(97 - 56*sqrt(3))) + pi*sqrt(97 - 56*sqrt(3))*sqrt(97 + 56*sqrt(3))/(49*sqrt(97 - 56*sqrt(3)) + 28*sqrt(3)*sqrt(97 - 56*sqrt(3))) + sqrt(97 - 56*sqrt(3))*sqrt(97 + 56*sqrt(3))*(-pi + atan(tan(1/2)/sqrt(97 + 56*sqrt(3))))/(49*sqrt(97 - 56*sqrt(3)) + 28*sqrt(3)*sqrt(97 - 56*sqrt(3)))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.