Sr Examen
Integral de (x+2)/((16+x^2)^(5/4)) dx
Solución
Ha introducido
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oo / | | x + 2 | ------------ dx | 5/4 | / 2\ | \16 + x / | / 0
$$\int\limits_{0}^{\infty} \frac{x + 2}{\left(x^{2} + 16\right)^{\frac{5}{4}}}\, dx$$
Integral((x + 2)/(16 + x^2)^(5/4), (x, 0, oo))
Respuesta (Indefinida)
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/ / | | | x + 2 2 | 1 | ------------ dx = C - ------------ + 2* | --------------------------------- dx | 5/4 _________ | _________ _________ | / 2\ 4 / 2 | 4 / 2 2 4 / 2 | \16 + x / \/ 16 + x | 16*\/ 16 + x + x *\/ 16 + x | | / /
$$\int \frac{x + 2}{\left(x^{2} + 16\right)^{\frac{5}{4}}}\, dx = C + 2 \int \frac{1}{x^{2} \sqrt[4]{x^{2} + 16} + 16 \sqrt[4]{x^{2} + 16}}\, dx - \frac{2}{\sqrt[4]{x^{2} + 16}}$$
Respuesta
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____ Gamma(1/4) \/ pi *Gamma(3/4) ------------ + ----------------- 4*Gamma(5/4) 8*Gamma(5/4)
$$\frac{\sqrt{\pi} \Gamma\left(\frac{3}{4}\right)}{8 \Gamma\left(\frac{5}{4}\right)} + \frac{\Gamma\left(\frac{1}{4}\right)}{4 \Gamma\left(\frac{5}{4}\right)}$$
=
=
____ Gamma(1/4) \/ pi *Gamma(3/4) ------------ + ----------------- 4*Gamma(5/4) 8*Gamma(5/4)
$$\frac{\sqrt{\pi} \Gamma\left(\frac{3}{4}\right)}{8 \Gamma\left(\frac{5}{4}\right)} + \frac{\Gamma\left(\frac{1}{4}\right)}{4 \Gamma\left(\frac{5}{4}\right)}$$
gamma(1/4)/(4*gamma(5/4)) + sqrt(pi)*gamma(3/4)/(8*gamma(5/4))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.