Sr Examen
Integral de sin^2(3x)/(x^4)^(1/3) dx
Solución
Ha introducido
[src]
oo / | | 2 | sin (3*x) | --------- dx | ____ | 3 / 4 | \/ x | / 0
$$\int\limits_{0}^{\infty} \frac{\sin^{2}{\left(3 x \right)}}{\sqrt[3]{x^{4}}}\, dx$$
Integral(sin(3*x)^2/(x^4)^(1/3), (x, 0, oo))
Respuesta (Indefinida)
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/ / | | | 2 | 2 | sin (3*x) | sin (3*x) | --------- dx = C + | --------- dx | ____ | ____ | 3 / 4 | 3 / 4 | \/ x | \/ x | | / /
$$\int \frac{\sin^{2}{\left(3 x \right)}}{\sqrt[3]{x^{4}}}\, dx = C + \int \frac{\sin^{2}{\left(3 x \right)}}{\sqrt[3]{x^{4}}}\, dx$$
Gráfica
Respuesta
[src]
2/3 3 ___
pi*2 *\/ 3 *Gamma(1/3)*Gamma(5/6)
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2
4*Gamma (2/3)*Gamma(7/6)
$$\frac{2^{\frac{2}{3}} \sqrt[3]{3} \pi \Gamma\left(\frac{1}{3}\right) \Gamma\left(\frac{5}{6}\right)}{4 \Gamma^{2}\left(\frac{2}{3}\right) \Gamma\left(\frac{7}{6}\right)}$$
=
=
2/3 3 ___
pi*2 *\/ 3 *Gamma(1/3)*Gamma(5/6)
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2
4*Gamma (2/3)*Gamma(7/6)
$$\frac{2^{\frac{2}{3}} \sqrt[3]{3} \pi \Gamma\left(\frac{1}{3}\right) \Gamma\left(\frac{5}{6}\right)}{4 \Gamma^{2}\left(\frac{2}{3}\right) \Gamma\left(\frac{7}{6}\right)}$$
pi*2^(2/3)*3^(1/3)*gamma(1/3)*gamma(5/6)/(4*gamma(2/3)^2*gamma(7/6))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.