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