Thread: calculate

CALCULATE THIS INTEGRAL :

Wolfram's The Integrator returns the following:

Code:

(x + Log[Cos[x] - Sin[x]] + 
 
    (4 Sqrt[Cos[x]] ((1 - I) 
 
                                          x
          EllipticPi[-I, -ArcSin[Sqrt[Tan[-]]], -1] + 
                                          2
 
                                                x
         (1 + I) EllipticPi[I, -ArcSin[Sqrt[Tan[-]]], 
                                                2
 
                                 1
           -1] - EllipticPi[------------, 
                            -1 + Sqrt[2]
 
                           x
          -ArcSin[Sqrt[Tan[-]]], -1] - 
                           2
 
                           1
         EllipticPi[-(-----------), 
                      1 + Sqrt[2]
 
                           x                   x
          -ArcSin[Sqrt[Tan[-]]], -1]) Sqrt[Tan[-]]) / 
                           2                   2
 
                      x 2
     (Sqrt[Cos[x] Sec[-] ] Sqrt[Sin[x]])) / 2
                      2

no, no, these integrals are made to solve them without computing the antiderivative since in many cases you won't be able to find it.

work a general problem and compute