Sr Examen
Integral de sin(x)*log(x)/x dx
Solución
Ha introducido
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1 / | | sin(x)*log(x) | ------------- dx | x | / 0
$$\int\limits_{0}^{1} \frac{\log{\left(x \right)} \sin{\left(x \right)}}{x}\, dx$$
Integral((sin(x)*log(x))/x, (x, 0, 1))
Respuesta (Indefinida)
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/ | _ / | 2 \ | sin(x)*log(x) |_ | 1/2, 1/2 | -x | | ------------- dx = C + Si(x)*log(x) - x* | | | ----| | x 2 3 \3/2, 3/2, 3/2 | 4 / | /
$$\int \frac{\log{\left(x \right)} \sin{\left(x \right)}}{x}\, dx = C - x {{}_{2}F_{3}\left(\begin{matrix} \frac{1}{2}, \frac{1}{2} \\ \frac{3}{2}, \frac{3}{2}, \frac{3}{2} \end{matrix}\middle| {- \frac{x^{2}}{4}} \right)} + \log{\left(x \right)} \operatorname{Si}{\left(x \right)}$$
Respuesta
[src]
_ |_ / 1/2, 1/2 | \ - | | | -1/4| 2 3 \3/2, 3/2, 3/2 | /
$$- {{}_{2}F_{3}\left(\begin{matrix} \frac{1}{2}, \frac{1}{2} \\ \frac{3}{2}, \frac{3}{2}, \frac{3}{2} \end{matrix}\middle| {- \frac{1}{4}} \right)}$$
=
=
_ |_ / 1/2, 1/2 | \ - | | | -1/4| 2 3 \3/2, 3/2, 3/2 | /
$$- {{}_{2}F_{3}\left(\begin{matrix} \frac{1}{2}, \frac{1}{2} \\ \frac{3}{2}, \frac{3}{2}, \frac{3}{2} \end{matrix}\middle| {- \frac{1}{4}} \right)}$$
-hyper((1/2, 1/2), (3/2, 3/2, 3/2), -1/4)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.