Sr Examen
Integral de 1/x*cos(sqr(x))*ln(x) dx
Solución
Ha introducido
[src]
1 / | | / 2\ | cos\x / | -------*log(x) dx | x | / 0
$$\int\limits_{0}^{1} \frac{\cos{\left(x^{2} \right)}}{x} \log{\left(x \right)}\, dx$$
Integral((cos(x^2)/x)*log(x), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ _ / | 4 \ | 4 |_ | 1, 1, 1 | -x | | / 2\ 2/ 4\ / 2\ / 4\ x * | | | ----| | cos\x / log \x / Ci\x /*log(x) EulerGamma*log\x / 3 4 \3/2, 2, 2, 2 | 4 / | -------*log(x) dx = C - -------- + ------------- - ------------------ + ----------------------------- | x 32 2 8 32 | /
$$\int \frac{\cos{\left(x^{2} \right)}}{x} \log{\left(x \right)}\, dx = C + \frac{x^{4} {{}_{3}F_{4}\left(\begin{matrix} 1, 1, 1 \\ \frac{3}{2}, 2, 2, 2 \end{matrix}\middle| {- \frac{x^{4}}{4}} \right)}}{32} + \frac{\log{\left(x \right)} \operatorname{Ci}{\left(x^{2} \right)}}{2} - \frac{\log{\left(x^{4} \right)}^{2}}{32} - \frac{\gamma \log{\left(x^{4} \right)}}{8}$$
Respuesta
[src]
_
|_ / 1, 1, 1 | \
| | | -1/4|
3 4 \3/2, 2, 2, 2 | /
-oo + --------------------------
32
$$\frac{{{}_{3}F_{4}\left(\begin{matrix} 1, 1, 1 \\ \frac{3}{2}, 2, 2, 2 \end{matrix}\middle| {- \frac{1}{4}} \right)}}{32} - \infty$$
=
=
_
|_ / 1, 1, 1 | \
| | | -1/4|
3 4 \3/2, 2, 2, 2 | /
-oo + --------------------------
32
$$\frac{{{}_{3}F_{4}\left(\begin{matrix} 1, 1, 1 \\ \frac{3}{2}, 2, 2, 2 \end{matrix}\middle| {- \frac{1}{4}} \right)}}{32} - \infty$$
-oo + hyper((1, 1, 1), (3/2, 2, 2, 2), -1/4)/32
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.