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