Sr Examen
Integral de sqrt(x)×arcsin(x) dx
Solución
Ha introducido
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1 / | | ___ | \/ x *asin(x) dx | / 0
$$\int\limits_{0}^{1} \sqrt{x} \operatorname{asin}{\left(x \right)}\, dx$$
Integral(sqrt(x)*asin(x), (x, 0, 1))
Respuesta (Indefinida)
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_ / 5/2 |_ /1/2, 5/4 | 2 2*pi*I\ | 3/2 x *Gamma(5/4)* | | | x *e | | ___ 2*x *asin(x) 2 1 \ 9/4 | / | \/ x *asin(x) dx = C + -------------- - -------------------------------------------- | 3 3*Gamma(9/4) /
$$\int \sqrt{x} \operatorname{asin}{\left(x \right)}\, dx = C - \frac{x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {x^{2} e^{2 i \pi}} \right)}}{3 \Gamma\left(\frac{9}{4}\right)} + \frac{2 x^{\frac{3}{2}} \operatorname{asin}{\left(x \right)}}{3}$$
Gráfica
Respuesta
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_
|_ /1/2, 5/4 | \
Gamma(5/4)* | | | 1|
pi 2 1 \ 9/4 | /
-- - ------------------------------
3 3*Gamma(9/4)
$$- \frac{\Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {1} \right)}}{3 \Gamma\left(\frac{9}{4}\right)} + \frac{\pi}{3}$$
=
=
_
|_ /1/2, 5/4 | \
Gamma(5/4)* | | | 1|
pi 2 1 \ 9/4 | /
-- - ------------------------------
3 3*Gamma(9/4)
$$- \frac{\Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {1} \right)}}{3 \Gamma\left(\frac{9}{4}\right)} + \frac{\pi}{3}$$
pi/3 - gamma(5/4)*hyper((1/2, 5/4), (9/4,), 1)/(3*gamma(9/4))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.