Sr Examen
Integral de sin(2*x)/sqrt(x^3+4) dx
Solución
Ha introducido
[src]
oo / | | sin(2*x) | ----------- dx | ________ | / 3 | \/ x + 4 | / 0
$$\int\limits_{0}^{\infty} \frac{\sin{\left(2 x \right)}}{\sqrt{x^{3} + 4}}\, dx$$
Integral(sin(2*x)/sqrt(x^3 + 4), (x, 0, oo))
Respuesta (Indefinida)
[src]
/ / | | | sin(2*x) | cos(x)*sin(x) | ----------- dx = C + 2* | ------------- dx | ________ | ________ | / 3 | / 3 | \/ x + 4 | \/ 4 + x | | / /
$$\int \frac{\sin{\left(2 x \right)}}{\sqrt{x^{3} + 4}}\, dx = C + 2 \int \frac{\sin{\left(x \right)} \cos{\left(x \right)}}{\sqrt{x^{3} + 4}}\, dx$$
Respuesta
[src]
6 ___ ___ __5, 2 / 5/6, 1/3 | 16\
\/ 2 *\/ 3 */__ | | ---|
\_|2, 8 \7/12, 1/12, 1/6, 1/2, 5/6 0, 1/3, 2/3 | 729/
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12*pi
$$\frac{\sqrt[6]{2} \sqrt{3} {G_{2, 8}^{5, 2}\left(\begin{matrix} \frac{5}{6}, \frac{1}{3} & \\\frac{7}{12}, \frac{1}{12}, \frac{1}{6}, \frac{1}{2}, \frac{5}{6} & 0, \frac{1}{3}, \frac{2}{3} \end{matrix} \middle| {\frac{16}{729}} \right)}}{12 \pi}$$
=
=
6 ___ ___ __5, 2 / 5/6, 1/3 | 16\
\/ 2 *\/ 3 */__ | | ---|
\_|2, 8 \7/12, 1/12, 1/6, 1/2, 5/6 0, 1/3, 2/3 | 729/
------------------------------------------------------------------
12*pi
$$\frac{\sqrt[6]{2} \sqrt{3} {G_{2, 8}^{5, 2}\left(\begin{matrix} \frac{5}{6}, \frac{1}{3} & \\\frac{7}{12}, \frac{1}{12}, \frac{1}{6}, \frac{1}{2}, \frac{5}{6} & 0, \frac{1}{3}, \frac{2}{3} \end{matrix} \middle| {\frac{16}{729}} \right)}}{12 \pi}$$
2^(1/6)*sqrt(3)*meijerg(((5/6, 1/3), ()), ((7/12, 1/12, 1/6, 1/2, 5/6), (0, 1/3, 2/3)), 16/729)/(12*pi)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.