Sr Examen
Integral de (cosx)/(1+cosx-sinx) dx
Solución
Ha introducido
[src]
0 / | | cos(x) | ------------------- dx | 1 + cos(x) - sin(x) | / -pi ---- 15
$$\int\limits_{- \frac{\pi}{15}}^{0} \frac{\cos{\left(x \right)}}{\left(\cos{\left(x \right)} + 1\right) - \sin{\left(x \right)}}\, dx$$
Integral(cos(x)/(1 + cos(x) - sin(x)), (x, -pi/15, 0))
Respuesta (Indefinida)
[src]
/ / 2/x\\ | log|1 + tan |-|| | cos(x) x \ \2// | ------------------- dx = C + - + ---------------- | 1 + cos(x) - sin(x) 2 2 | /
$$\int \frac{\cos{\left(x \right)}}{\left(\cos{\left(x \right)} + 1\right) - \sin{\left(x \right)}}\, dx = C + \frac{x}{2} + \frac{\log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)}}{2}$$
Gráfica
Respuesta
[src]
/ 2\
| / ___________\ |
| | / ___ | |
| | ___ / 5 \/ 5 | |
| | ___ \/ 3 * / - + ----- | |
| | 1 \/ 5 \/ 8 8 | |
| | - - + ----- + ----------------------| |
| | 1 8 8 2 | |
log|1 + |- ------------------------------------ + ------------------------------------| |
| | ___________ ___________ | |
| | / ___ / ___\ / ___ / ___\| |
| | / 5 \/ 5 ___ |1 \/ 5 | / 5 \/ 5 ___ |1 \/ 5 || |
| | / - + ----- \/ 3 *|- - -----| / - + ----- \/ 3 *|- - -----|| |
| | \/ 8 8 \4 4 / \/ 8 8 \4 4 /| |
| | ---------------- + ----------------- ---------------- + -----------------| |
\ \ 2 2 2 2 / / pi
- ----------------------------------------------------------------------------------------- + --
2 30
$$- \frac{\log{\left(\left(- \frac{1}{\frac{\sqrt{3} \left(\frac{1}{4} - \frac{\sqrt{5}}{4}\right)}{2} + \frac{\sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{2}} + \frac{- \frac{1}{8} + \frac{\sqrt{5}}{8} + \frac{\sqrt{3} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{2}}{\frac{\sqrt{3} \left(\frac{1}{4} - \frac{\sqrt{5}}{4}\right)}{2} + \frac{\sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{2}}\right)^{2} + 1 \right)}}{2} + \frac{\pi}{30}$$
=
=
/ 2\
| / ___________\ |
| | / ___ | |
| | ___ / 5 \/ 5 | |
| | ___ \/ 3 * / - + ----- | |
| | 1 \/ 5 \/ 8 8 | |
| | - - + ----- + ----------------------| |
| | 1 8 8 2 | |
log|1 + |- ------------------------------------ + ------------------------------------| |
| | ___________ ___________ | |
| | / ___ / ___\ / ___ / ___\| |
| | / 5 \/ 5 ___ |1 \/ 5 | / 5 \/ 5 ___ |1 \/ 5 || |
| | / - + ----- \/ 3 *|- - -----| / - + ----- \/ 3 *|- - -----|| |
| | \/ 8 8 \4 4 / \/ 8 8 \4 4 /| |
| | ---------------- + ----------------- ---------------- + -----------------| |
\ \ 2 2 2 2 / / pi
- ----------------------------------------------------------------------------------------- + --
2 30
$$- \frac{\log{\left(\left(- \frac{1}{\frac{\sqrt{3} \left(\frac{1}{4} - \frac{\sqrt{5}}{4}\right)}{2} + \frac{\sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{2}} + \frac{- \frac{1}{8} + \frac{\sqrt{5}}{8} + \frac{\sqrt{3} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{2}}{\frac{\sqrt{3} \left(\frac{1}{4} - \frac{\sqrt{5}}{4}\right)}{2} + \frac{\sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{2}}\right)^{2} + 1 \right)}}{2} + \frac{\pi}{30}$$
-log(1 + (-1/(sqrt(5/8 + sqrt(5)/8)/2 + sqrt(3)*(1/4 - sqrt(5)/4)/2) + (-1/8 + sqrt(5)/8 + sqrt(3)*sqrt(5/8 + sqrt(5)/8)/2)/(sqrt(5/8 + sqrt(5)/8)/2 + sqrt(3)*(1/4 - sqrt(5)/4)/2))^2)/2 + pi/30
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.