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

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

(a*x - Sqrt[b]*ArcTan[Tan[a*x]/Sqrt[b]])/(a - a*b)


Integrate[Tan[a*x]^2/(b + Tan[a*x]^2), x] ==
(a*x - Sqrt[b]*ArcTan[Tan[a*x]/Sqrt[b]])/(a - a*b)



                    2
            Tan[a x]
Integrate[-------------, x] == 
                      2
          b + Tan[a x]

                     Tan[a x]
a x - Sqrt[b] ArcTan[--------]
                     Sqrt[b]
------------------------------
           a - a b

Time to compute: 0.10 second

Spread the word: