Integral de (sqrt(x))*cos(pi*n*x) dx

                                                                                                                                                
                                                                                    ___                         _  /              |    2  2  2 \
  /                                                                    ___  3/2    / 1                         |_  |   1/4, 3/4   | -pi *n *x  |
 |                                        ___                        \/ n *x   *  /  - *Gamma(1/4)*Gamma(3/4)* |   |              | -----------|
 |   ___                          ___    / 1   /  ___   ___   ___\              \/   n                        2  3 \1/2, 5/4, 7/4 |      4     /
 | \/ x *cos(pi*n*x) dx = C + x*\/ 2 *  /  - *C\\/ 2 *\/ n *\/ x / - ---------------------------------------------------------------------------
 |                                    \/   n                                                   4*Gamma(5/4)*Gamma(7/4)                          
/                                                                                                                                               

$$\int \sqrt{x} \cos{\left(x \pi n \right)}\, dx = C - \frac{\sqrt{n} x^{\frac{3}{2}} \sqrt{\frac{1}{n}} \Gamma\left(\frac{1}{4}\right) \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{3}\left(\begin{matrix} \frac{1}{4}, \frac{3}{4} \\ \frac{1}{2}, \frac{5}{4}, \frac{7}{4} \end{matrix}\middle| {- \frac{\pi^{2} n^{2} x^{2}}{4}} \right)}}{4 \Gamma\left(\frac{5}{4}\right) \Gamma\left(\frac{7}{4}\right)} + \sqrt{2} x \sqrt{\frac{1}{n}} C\left(\sqrt{2} \sqrt{n} \sqrt{x}\right)$$

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