Sr Examen
Integral de (x^2-sin(x^2))/(x*(x^0.5)) dx
Solución
Ha introducido
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1 / | | 2 / 2\ | x - sin\x / | ------------ dx | ___ | x*\/ x | / 0
$$\int\limits_{0}^{1} \frac{x^{2} - \sin{\left(x^{2} \right)}}{\sqrt{x} x}\, dx$$
Integral((x^2 - sin(x^2))/((x*sqrt(x))), (x, 0, 1))
Respuesta (Indefinida)
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/ _ / | 4 \ | 3/2 |_ | 3/8 | -x | | 2 / 2\ 3/2 x *Gamma(3/8)* | | | ----| | x - sin\x / 2*x 1 2 \11/8, 3/2 | 4 / | ------------ dx = C + ------ - --------------------------------------- | ___ 3 4*Gamma(11/8) | x*\/ x | /
$$\int \frac{x^{2} - \sin{\left(x^{2} \right)}}{\sqrt{x} x}\, dx = C - \frac{x^{\frac{3}{2}} \Gamma\left(\frac{3}{8}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{3}{8} \\ \frac{11}{8}, \frac{3}{2} \end{matrix}\middle| {- \frac{x^{4}}{4}} \right)}}{4 \Gamma\left(\frac{11}{8}\right)} + \frac{2 x^{\frac{3}{2}}}{3}$$
Respuesta
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_
|_ / 3/8 | \
Gamma(3/8)* | | | -1/4|
2 1 2 \11/8, 3/2 | /
- - ----------------------------------
3 4*Gamma(11/8)
$$- \frac{\Gamma\left(\frac{3}{8}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{3}{8} \\ \frac{11}{8}, \frac{3}{2} \end{matrix}\middle| {- \frac{1}{4}} \right)}}{4 \Gamma\left(\frac{11}{8}\right)} + \frac{2}{3}$$
=
=
_
|_ / 3/8 | \
Gamma(3/8)* | | | -1/4|
2 1 2 \11/8, 3/2 | /
- - ----------------------------------
3 4*Gamma(11/8)
$$- \frac{\Gamma\left(\frac{3}{8}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{3}{8} \\ \frac{11}{8}, \frac{3}{2} \end{matrix}\middle| {- \frac{1}{4}} \right)}}{4 \Gamma\left(\frac{11}{8}\right)} + \frac{2}{3}$$
2/3 - gamma(3/8)*hyper((3/8,), (11/8, 3/2), -1/4)/(4*gamma(11/8))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.