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