integrals.wolfram.com   Use one of Mathematica's 2500+ functions FREE online

Wolfram Mathematica Online Integrator
The world's only full-power integration solver
∫

An image showing the results of your requested integral.


Integrate[x/(Cos[x] + Sin[x]), x] ==
(-(Pi*ArcTanh[(-1 + Tan[x/2])/Sqrt[2]]) + 2*((Pi/4 + x)*(Log[1 - (-1)^(1/4)*E^(I*x)] - Log[1 + E^((I/4)*(Pi + 4*x))]) + I*(PolyLog[2, -((-1)^(1/4)*E^(I*x))] - PolyLog[2, E^((I/4)*(Pi + 4*x))])))/(2*Sqrt[2])



                 x
Integrate[---------------, x] == 
          Cos[x] + Sin[x]

                       x
              -1 + Tan[-]
                       2
(-(Pi ArcTanh[-----------]) + 
                Sqrt[2]
 
        Pi                   1/4  I x
    2 ((-- + x) (Log[1 - (-1)    E   ] - 
        4
 
                   I/4 (Pi + 4 x)
          Log[1 + E              ]) + 
 
                           1/4  I x
       I (PolyLog[2, -((-1)    E   )] - 
 
                      I/4 (Pi + 4 x)
          PolyLog[2, E              ]))) / (2 Sqrt[2])

Time to compute: 0.19 second

Spread the word: