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^4/(1 + E^(a*x)), x] ==
x^5/5 - (x^4*Log[1 + E^(a*x)])/a - (4*x^3*PolyLog[2, -E^(a*x)])/a^2 + (12*x^2*PolyLog[3, -E^(a*x)])/a^3 - (24*x*PolyLog[4, -E^(a*x)])/a^4 + (24*PolyLog[5, -E^(a*x)])/a^5



              4
             x
Integrate[--------, x] == 
               a x
          1 + E

 5    4          a x       3              a x
x    x  Log[1 + E   ]   4 x  PolyLog[2, -E   ]
-- - ---------------- - ---------------------- + 
5           a                      2
                                  a
 
      2              a x                      a x
  12 x  PolyLog[3, -E   ]   24 x PolyLog[4, -E   ]
  ----------------------- - ---------------------- + 
             3                         4
            a                         a
 
                  a x
  24 PolyLog[5, -E   ]
  --------------------
            5
           a

Time to compute: 0.01 second

Spread the word: