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sqrt(x)*sin(x)
Solving integrals/ sqrt(x)*sin(x)

Integral of sqrt(x)*sin(x) dx

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The solution

You have entered [src] 
  1                
  /                
 |                 
 |    ___          
 |  \/ x *sin(x) dx
 |                 
/                  
0
$$\int\limits_{0}^{1} \sqrt{x} \sin{\left(x \right)}\, dx$$ 
Integral(sqrt(x)*sin(x), (x, 0, 1))
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)              
/
$$\int \sqrt{x} \sin{\left(x \right)}\, dx = C - \frac{5 \sqrt{x} \cos{\left(x \right)} \Gamma\left(\frac{5}{4}\right)}{4 \Gamma\left(\frac{9}{4}\right)} + \frac{5 \sqrt{2} \sqrt{\pi} C\left(\frac{\sqrt{2} \sqrt{x}}{\sqrt{\pi}}\right) \Gamma\left(\frac{5}{4}\right)}{8 \Gamma\left(\frac{9}{4}\right)}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
                                        /  ___ \           
                            ___   ____  |\/ 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)
$$- \frac{5 \cos{\left(1 \right)} \Gamma\left(\frac{5}{4}\right)}{4 \Gamma\left(\frac{9}{4}\right)} + \frac{5 \sqrt{2} \sqrt{\pi} C\left(\frac{\sqrt{2}}{\sqrt{\pi}}\right) \Gamma\left(\frac{5}{4}\right)}{8 \Gamma\left(\frac{9}{4}\right)}$$
Упростить
Numerical answer [src] 
0.364221932032132
0.364221932032132
The graph
Integral of sqrt(x)*sin(x) dx

    Use the examples entering the upper and lower limits of integration.

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