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

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

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The solution

You have entered [src] 
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 |  \/ x *cos(x) dx
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0
∫01xcos⁡(x) dx\int\limits_{0}^{1} \sqrt{x} \cos{\left(x \right)}\, dx
Simplify
The answer (Indefinite) [src] 
                                                                     /  ___   ___\           
                                                         ___   ____  |\/ 2 *\/ x |           
  /                                                  3*\/ 2 *\/ pi *S|-----------|*Gamma(3/4)
 |                           ___                                     |     ____  |           
 |   ___                 3*\/ x *Gamma(3/4)*sin(x)                   \   \/ pi   /           
 | \/ x *cos(x) dx = C + ------------------------- - ----------------------------------------
 |                              4*Gamma(7/4)                       8*Gamma(7/4)              
/
−π ((2 i+2) erf((2 i+2) x2)+(2 i−2) erf((2 i−2) x2)+(2−2 i) erf(−i x)+(2 i+2) erf((−1)14 x))−16 x sin⁡x16-{{\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}-\sqrt{2}\,i\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)-16\, \sqrt{x}\,\sin x}\over{16}}
Simplify
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  |           
                      3*\/ 2 *\/ pi *S|------|*Gamma(3/4)
                                      |  ____|           
3*Gamma(3/4)*sin(1)                   \\/ pi /           
------------------- - -----------------------------------
    4*Gamma(7/4)                  8*Gamma(7/4)
−π ((2 i+2) erf(2 i+22)+(2 i−2) erf(2 i−22)+(2−2 i) erf(−i)+(2 i+2) erf((−1)14))−16 sin⁡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}-\sqrt{2}\,i\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\, \sin 1}\over{16}} 
=
= 
                                      /  ___ \           
                          ___   ____  |\/ 2  |           
                      3*\/ 2 *\/ pi *S|------|*Gamma(3/4)
                                      |  ____|           
3*Gamma(3/4)*sin(1)                   \\/ pi /           
------------------- - -----------------------------------
    4*Gamma(7/4)                  8*Gamma(7/4)
−32πS(2π)Γ(34)8Γ(74)+3sin⁡(1)Γ(34)4Γ(74)- \frac{3 \sqrt{2} \sqrt{\pi} S\left(\frac{\sqrt{2}}{\sqrt{\pi}}\right) \Gamma\left(\frac{3}{4}\right)}{8 \Gamma\left(\frac{7}{4}\right)} + \frac{3 \sin{\left(1 \right)} \Gamma\left(\frac{3}{4}\right)}{4 \Gamma\left(\frac{7}{4}\right)}
Simplify
Numerical answer [src] 
0.531202683084515
0.531202683084515
The graph
Integral of sqrt(x)*cos(x) dx

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

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