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(xsenx)/√x
Solving integrals/ (xsenx)/√x

Integral of (xsenx)/√x dx

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You have entered [src] 
  1            
  /            
 |             
 |  x*sin(x)   
 |  -------- dx
 |     ___     
 |   \/ x      
 |             
/              
0
∫01xsin⁡(x)x dx\int\limits_{0}^{1} \frac{x \sin{\left(x \right)}}{\sqrt{x}}\, dx 
Integral(x*sin(x)/(sqrt(x)), (x, 0, 1))
The answer (Indefinite) [src] 
  /                    /               
 |                    |                
 | x*sin(x)           |   ___          
 | -------- dx = C +  | \/ x *sin(x) dx
 |    ___             |                
 |  \/ x             /                 
 |                                     
/
−16 x cos⁡x+π ((2 i−2) erf((2 i+2) x2)+(2 i+2) erf((2 i−2) x2)+(−2 i−2) erf(−i x)+(2 i−2) erf((−1)14 x))16-{{16\,\sqrt{x}\,\cos x+\sqrt{\pi}\,\left(\left(\sqrt{2}\,i-\sqrt{2 }\right)\,\mathrm{erf}\left({{\left(\sqrt{2}\,i+\sqrt{2}\right)\, \sqrt{x}}\over{2}}\right)+\left(\sqrt{2}\,i+\sqrt{2}\right)\, \mathrm{erf}\left({{\left(\sqrt{2}\,i-\sqrt{2}\right)\,\sqrt{x} }\over{2}}\right)+\left(-\sqrt{2}\,i-\sqrt{2}\right)\,\mathrm{erf} \left(\sqrt{-i}\,\sqrt{x}\right)+\left(\sqrt{2}\,i-\sqrt{2}\right)\, \mathrm{erf}\left(\left(-1\right)^{{{1}\over{4}}}\,\sqrt{x}\right) \right)}\over{16}}
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The graph
0.001.000.100.200.300.400.500.600.700.800.900.01.0
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)
−π ((2 i−2) erf(2 i+22)+(2 i+2) erf(2 i−22)+(−2 i−2) erf(−i)+(2 i−2) erf((−1)14))+16 cos⁡116-{{\sqrt{\pi}\,\left(\left(\sqrt{2}\,i-\sqrt{2}\right)\, \mathrm{erf}\left({{\sqrt{2}\,i+\sqrt{2}}\over{2}}\right)+\left( \sqrt{2}\,i+\sqrt{2}\right)\,\mathrm{erf}\left({{\sqrt{2}\,i-\sqrt{2 }}\over{2}}\right)+\left(-\sqrt{2}\,i-\sqrt{2}\right)\,\mathrm{erf} \left(\sqrt{-i}\right)+\left(\sqrt{2}\,i-\sqrt{2}\right)\, \mathrm{erf}\left(\left(-1\right)^{{{1}\over{4}}}\right)\right)+16\, \cos 1}\over{16}} 
=
= 
                                        /  ___ \           
                            ___   ____  |\/ 2  |           
                        5*\/ 2 *\/ pi *C|------|*Gamma(5/4)
                                        |  ____|           
  5*cos(1)*Gamma(5/4)                   \\/ pi /           
- ------------------- + -----------------------------------
      4*Gamma(9/4)                  8*Gamma(9/4)
−5cos⁡(1)Γ(54)4Γ(94)+52πC(2π)Γ(54)8Γ(94)- \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)}
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Numerical answer [src] 
0.364221932032132
0.364221932032132
The graph
Integral of (xsenx)/√x dx

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

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