Integral of sqrt(x)*sin(x) dx
The solution
The answer (Indefinite)
[src]
/ ___ ___\
___ ____ |\/ 2 *\/ x |
/ 5*\/ 2 *\/ pi *C|-----------|*Gamma(5/4)
| ___ | ____ |
| ___ 5*\/ x *cos(x)*Gamma(5/4) \ \/ pi /
| \/ x *sin(x) dx = C - ------------------------- + ----------------------------------------
| 4*Gamma(9/4) 8*Gamma(9/4)
/
$$\int \sqrt{x} \sin{\left(x \right)}\, dx = C - \frac{5 \sqrt{x} \cos{\left(x \right)} \Gamma\left(\frac{5}{4}\right)}{4 \Gamma\left(\frac{9}{4}\right)} + \frac{5 \sqrt{2} \sqrt{\pi} C\left(\frac{\sqrt{2} \sqrt{x}}{\sqrt{\pi}}\right) \Gamma\left(\frac{5}{4}\right)}{8 \Gamma\left(\frac{9}{4}\right)}$$
/ ___ \
___ ____ |\/ 2 |
5*\/ 2 *\/ pi *C|------|*Gamma(5/4)
| ____|
5*cos(1)*Gamma(5/4) \\/ pi /
- ------------------- + -----------------------------------
4*Gamma(9/4) 8*Gamma(9/4)
$$- \frac{5 \cos{\left(1 \right)} \Gamma\left(\frac{5}{4}\right)}{4 \Gamma\left(\frac{9}{4}\right)} + \frac{5 \sqrt{2} \sqrt{\pi} C\left(\frac{\sqrt{2}}{\sqrt{\pi}}\right) \Gamma\left(\frac{5}{4}\right)}{8 \Gamma\left(\frac{9}{4}\right)}$$
=
/ ___ \
___ ____ |\/ 2 |
5*\/ 2 *\/ pi *C|------|*Gamma(5/4)
| ____|
5*cos(1)*Gamma(5/4) \\/ pi /
- ------------------- + -----------------------------------
4*Gamma(9/4) 8*Gamma(9/4)
$$- \frac{5 \cos{\left(1 \right)} \Gamma\left(\frac{5}{4}\right)}{4 \Gamma\left(\frac{9}{4}\right)} + \frac{5 \sqrt{2} \sqrt{\pi} C\left(\frac{\sqrt{2}}{\sqrt{\pi}}\right) \Gamma\left(\frac{5}{4}\right)}{8 \Gamma\left(\frac{9}{4}\right)}$$
Use the examples entering the upper and lower limits of integration.