Integration Mania Continued

Calculus Level 5

1313x41x4arccos(2x1+x2)dx \large \int_{-\frac1{\sqrt3}}^{\frac1{\sqrt3}} \dfrac{x^4}{1-x^4} \text{arccos} \left( \dfrac{2x}{1+x^2} \right) \, dx

The integral above can be expressed as

πA[BCπDEFlnG+HGH], - \pi ^ A \left [ \dfrac B{\sqrt C} - \dfrac{\pi }{D} - \dfrac EF \ln \left |\dfrac{\sqrt G+ H}{\sqrt G - H} \right | \right ] ,

where A,B,C,D,E,F,G,HA,B,C,D,E,F,G,H are all positive integers with C,GC,G square-free and E,FE, F coprime.

Submit your answer as the sum A+B+C+D+E+F+G+H A + B + C + D + E + F + G + H .

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