Sr Examen
Integral de (1+sin(x))*1/(1-sin(x))^2 dx
Solución
Ha introducido
[src]
pi -- 4 / | | 1 + sin(x) | ------------- dx | 2 | (1 - sin(x)) | / 0
$$\int\limits_{0}^{\frac{\pi}{4}} \frac{\sin{\left(x \right)} + 1}{\left(1 - \sin{\left(x \right)}\right)^{2}}\, dx$$
Integral((1 + sin(x))/(1 - sin(x))^2, (x, 0, pi/4))
Respuesta (Indefinida)
[src]
/ 2/x\ | 6*tan |-| | 1 + sin(x) 2 \2/ | ------------- dx = C - ------------------------------------- - ------------------------------------- | 2 2/x\ 3/x\ /x\ 2/x\ 3/x\ /x\ | (1 - sin(x)) -3 - 9*tan |-| + 3*tan |-| + 9*tan|-| -3 - 9*tan |-| + 3*tan |-| + 9*tan|-| | \2/ \2/ \2/ \2/ \2/ \2/ /
$$\int \frac{\sin{\left(x \right)} + 1}{\left(1 - \sin{\left(x \right)}\right)^{2}}\, dx = C - \frac{6 \tan^{2}{\left(\frac{x}{2} \right)}}{3 \tan^{3}{\left(\frac{x}{2} \right)} - 9 \tan^{2}{\left(\frac{x}{2} \right)} + 9 \tan{\left(\frac{x}{2} \right)} - 3} - \frac{2}{3 \tan^{3}{\left(\frac{x}{2} \right)} - 9 \tan^{2}{\left(\frac{x}{2} \right)} + 9 \tan{\left(\frac{x}{2} \right)} - 3}$$
Gráfica
Respuesta
[src]
2
/ ___\
2 2 6*\-1 + \/ 2 /
- - - ------------------------------------------------- - -------------------------------------------------
3 2 3 2 3
/ ___\ / ___\ ___ / ___\ / ___\ ___
-12 - 9*\-1 + \/ 2 / + 3*\-1 + \/ 2 / + 9*\/ 2 -12 - 9*\-1 + \/ 2 / + 3*\-1 + \/ 2 / + 9*\/ 2
$$- \frac{2}{3} - \frac{6 \left(-1 + \sqrt{2}\right)^{2}}{-12 - 9 \left(-1 + \sqrt{2}\right)^{2} + 3 \left(-1 + \sqrt{2}\right)^{3} + 9 \sqrt{2}} - \frac{2}{-12 - 9 \left(-1 + \sqrt{2}\right)^{2} + 3 \left(-1 + \sqrt{2}\right)^{3} + 9 \sqrt{2}}$$
=
=
2
/ ___\
2 2 6*\-1 + \/ 2 /
- - - ------------------------------------------------- - -------------------------------------------------
3 2 3 2 3
/ ___\ / ___\ ___ / ___\ / ___\ ___
-12 - 9*\-1 + \/ 2 / + 3*\-1 + \/ 2 / + 9*\/ 2 -12 - 9*\-1 + \/ 2 / + 3*\-1 + \/ 2 / + 9*\/ 2
$$- \frac{2}{3} - \frac{6 \left(-1 + \sqrt{2}\right)^{2}}{-12 - 9 \left(-1 + \sqrt{2}\right)^{2} + 3 \left(-1 + \sqrt{2}\right)^{3} + 9 \sqrt{2}} - \frac{2}{-12 - 9 \left(-1 + \sqrt{2}\right)^{2} + 3 \left(-1 + \sqrt{2}\right)^{3} + 9 \sqrt{2}}$$
-2/3 - 2/(-12 - 9*(-1 + sqrt(2))^2 + 3*(-1 + sqrt(2))^3 + 9*sqrt(2)) - 6*(-1 + sqrt(2))^2/(-12 - 9*(-1 + sqrt(2))^2 + 3*(-1 + sqrt(2))^3 + 9*sqrt(2))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.