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