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