Sr Examen
Integral de sin(9x^2-5)*inxdx dx
Solución
Ha introducido
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1 / | | / 2 \ | sin\9*x - 5/*log(x) dx | / 0
$$\int\limits_{0}^{1} \log{\left(x \right)} \sin{\left(9 x^{2} - 5 \right)}\, dx$$
Integral(sin(9*x^2 - 5)*log(x), (x, 0, 1))
Respuesta (Indefinida)
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/ \
| _ / | 4\ _ / | 4\|
| ___ 2 |_ | 1/4, 1/4 | -81*x | ___ 3 2 |_ | 3/4, 3/4 | -81*x ||
| 3*x*\/ 2 *Gamma (1/4)* | | | ------|*sin(5) 27*\/ 2 *x *Gamma (3/4)*cos(5)* | | | ------|| / / ___\ / ___\ \
___ ____ | 2 3 \1/2, 5/4, 5/4 | 4 / 2 3 \3/2, 7/4, 7/4 | 4 /| ___ ____ | |3*x*\/ 2 | |3*x*\/ 2 | |
/ \/ 2 *\/ pi *|- ---------------------------------------------------------- + ------------------------------------------------------------| \/ 2 *\/ pi *|cos(5)*S|---------| - C|---------|*sin(5)|*log(x)
| | ____ 2 ____ 2 | | | ____ | | ____ | |
| / 2 \ \ 16*\/ pi *Gamma (5/4) 16*\/ pi *Gamma (7/4) / \ \ \/ pi / \ \/ pi / /
| sin\9*x - 5/*log(x) dx = C - ------------------------------------------------------------------------------------------------------------------------------------------ + ---------------------------------------------------------------
| 6 6
/
$$\int \log{\left(x \right)} \sin{\left(9 x^{2} - 5 \right)}\, dx = C + \frac{\sqrt{2} \sqrt{\pi} \left(- \sin{\left(5 \right)} C\left(\frac{3 \sqrt{2} x}{\sqrt{\pi}}\right) + \cos{\left(5 \right)} S\left(\frac{3 \sqrt{2} x}{\sqrt{\pi}}\right)\right) \log{\left(x \right)}}{6} - \frac{\sqrt{2} \sqrt{\pi} \left(\frac{27 \sqrt{2} x^{3} \cos{\left(5 \right)} \Gamma^{2}\left(\frac{3}{4}\right) {{}_{2}F_{3}\left(\begin{matrix} \frac{3}{4}, \frac{3}{4} \\ \frac{3}{2}, \frac{7}{4}, \frac{7}{4} \end{matrix}\middle| {- \frac{81 x^{4}}{4}} \right)}}{16 \sqrt{\pi} \Gamma^{2}\left(\frac{7}{4}\right)} - \frac{3 \sqrt{2} x \sin{\left(5 \right)} \Gamma^{2}\left(\frac{1}{4}\right) {{}_{2}F_{3}\left(\begin{matrix} \frac{1}{4}, \frac{1}{4} \\ \frac{1}{2}, \frac{5}{4}, \frac{5}{4} \end{matrix}\middle| {- \frac{81 x^{4}}{4}} \right)}}{16 \sqrt{\pi} \Gamma^{2}\left(\frac{5}{4}\right)}\right)}{6}$$
Gráfica
Respuesta
[src]
/ _ _ \
| ___ 2 |_ / 1/4, 1/4 | \ ___ 2 |_ / 3/4, 3/4 | \|
| 3*\/ 2 *Gamma (1/4)* | | | -81/4|*sin(5) 27*\/ 2 *Gamma (3/4)*cos(5)* | | | -81/4||
___ ____ | 2 3 \1/2, 5/4, 5/4 | / 2 3 \3/2, 7/4, 7/4 | /|
-\/ 2 *\/ pi *|- ------------------------------------------------------- + --------------------------------------------------------|
| ____ 2 ____ 2 |
\ 16*\/ pi *Gamma (5/4) 16*\/ pi *Gamma (7/4) /
-------------------------------------------------------------------------------------------------------------------------------------
6
$$- \frac{\sqrt{2} \sqrt{\pi} \left(- \frac{3 \sqrt{2} \sin{\left(5 \right)} \Gamma^{2}\left(\frac{1}{4}\right) {{}_{2}F_{3}\left(\begin{matrix} \frac{1}{4}, \frac{1}{4} \\ \frac{1}{2}, \frac{5}{4}, \frac{5}{4} \end{matrix}\middle| {- \frac{81}{4}} \right)}}{16 \sqrt{\pi} \Gamma^{2}\left(\frac{5}{4}\right)} + \frac{27 \sqrt{2} \cos{\left(5 \right)} \Gamma^{2}\left(\frac{3}{4}\right) {{}_{2}F_{3}\left(\begin{matrix} \frac{3}{4}, \frac{3}{4} \\ \frac{3}{2}, \frac{7}{4}, \frac{7}{4} \end{matrix}\middle| {- \frac{81}{4}} \right)}}{16 \sqrt{\pi} \Gamma^{2}\left(\frac{7}{4}\right)}\right)}{6}$$
=
=
/ _ _ \
| ___ 2 |_ / 1/4, 1/4 | \ ___ 2 |_ / 3/4, 3/4 | \|
| 3*\/ 2 *Gamma (1/4)* | | | -81/4|*sin(5) 27*\/ 2 *Gamma (3/4)*cos(5)* | | | -81/4||
___ ____ | 2 3 \1/2, 5/4, 5/4 | / 2 3 \3/2, 7/4, 7/4 | /|
-\/ 2 *\/ pi *|- ------------------------------------------------------- + --------------------------------------------------------|
| ____ 2 ____ 2 |
\ 16*\/ pi *Gamma (5/4) 16*\/ pi *Gamma (7/4) /
-------------------------------------------------------------------------------------------------------------------------------------
6
$$- \frac{\sqrt{2} \sqrt{\pi} \left(- \frac{3 \sqrt{2} \sin{\left(5 \right)} \Gamma^{2}\left(\frac{1}{4}\right) {{}_{2}F_{3}\left(\begin{matrix} \frac{1}{4}, \frac{1}{4} \\ \frac{1}{2}, \frac{5}{4}, \frac{5}{4} \end{matrix}\middle| {- \frac{81}{4}} \right)}}{16 \sqrt{\pi} \Gamma^{2}\left(\frac{5}{4}\right)} + \frac{27 \sqrt{2} \cos{\left(5 \right)} \Gamma^{2}\left(\frac{3}{4}\right) {{}_{2}F_{3}\left(\begin{matrix} \frac{3}{4}, \frac{3}{4} \\ \frac{3}{2}, \frac{7}{4}, \frac{7}{4} \end{matrix}\middle| {- \frac{81}{4}} \right)}}{16 \sqrt{\pi} \Gamma^{2}\left(\frac{7}{4}\right)}\right)}{6}$$
-sqrt(2)*sqrt(pi)*(-3*sqrt(2)*gamma(1/4)^2*hyper((1/4, 1/4), (1/2, 5/4, 5/4), -81/4)*sin(5)/(16*sqrt(pi)*gamma(5/4)^2) + 27*sqrt(2)*gamma(3/4)^2*cos(5)*hyper((3/4, 3/4), (3/2, 7/4, 7/4), -81/4)/(16*sqrt(pi)*gamma(7/4)^2))/6
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.