Sr Examen
Integral de sinInx/x dx
Solución
Ha introducido
[src]
E / | | sin(x)*log(x) | ------------- dx | x | / 1
$$\int\limits_{1}^{e} \frac{\log{\left(x \right)} \sin{\left(x \right)}}{x}\, dx$$
Integral((sin(x)*log(x))/x, (x, 1, E))
Respuesta (Indefinida)
[src]
/ | _ / | 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 / | /
$$\int \frac{\log{\left(x \right)} \sin{\left(x \right)}}{x}\, dx = C - x {{}_{2}F_{3}\left(\begin{matrix} \frac{1}{2}, \frac{1}{2} \\ \frac{3}{2}, \frac{3}{2}, \frac{3}{2} \end{matrix}\middle| {- \frac{x^{2}}{4}} \right)} + \log{\left(x \right)} \operatorname{Si}{\left(x \right)}$$
Gráfica
Respuesta
[src]
_ / | 2 \ _
|_ | 1/2, 1/2 | -e | |_ / 1/2, 1/2 | \
- E* | | | ----| + Si(E) + | | | -1/4|
2 3 \3/2, 3/2, 3/2 | 4 / 2 3 \3/2, 3/2, 3/2 | /
$${{}_{2}F_{3}\left(\begin{matrix} \frac{1}{2}, \frac{1}{2} \\ \frac{3}{2}, \frac{3}{2}, \frac{3}{2} \end{matrix}\middle| {- \frac{1}{4}} \right)} - e {{}_{2}F_{3}\left(\begin{matrix} \frac{1}{2}, \frac{1}{2} \\ \frac{3}{2}, \frac{3}{2}, \frac{3}{2} \end{matrix}\middle| {- \frac{e^{2}}{4}} \right)} + \operatorname{Si}{\left(e \right)}$$
=
=
_ / | 2 \ _
|_ | 1/2, 1/2 | -e | |_ / 1/2, 1/2 | \
- E* | | | ----| + Si(E) + | | | -1/4|
2 3 \3/2, 3/2, 3/2 | 4 / 2 3 \3/2, 3/2, 3/2 | /
$${{}_{2}F_{3}\left(\begin{matrix} \frac{1}{2}, \frac{1}{2} \\ \frac{3}{2}, \frac{3}{2}, \frac{3}{2} \end{matrix}\middle| {- \frac{1}{4}} \right)} - e {{}_{2}F_{3}\left(\begin{matrix} \frac{1}{2}, \frac{1}{2} \\ \frac{3}{2}, \frac{3}{2}, \frac{3}{2} \end{matrix}\middle| {- \frac{e^{2}}{4}} \right)} + \operatorname{Si}{\left(e \right)}$$
-E*hyper((1/2, 1/2), (3/2, 3/2, 3/2), -exp(2)/4) + Si(E) + 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.