The value of the integral∫−1/31/3 x41−x4cos−1⁡2x1+x2dx is

∫−1/31/3 x41−x4cos−1⁡2x1+x2dx=∫−1/31/3 x41−x4π2−sin−1⁡2x1+x2dx=π2∫−1/31/3 x41−x4dxsin−1⁡(−x)=−sin−1⁡x so the last integral is zero)=π∫01/3 −1+11−x4dx=π∫01/3 −1+1211−x2+11+x2dx=−π3+π212log⁡1+x1−x+tan−1⁡x01/3=−π3+π212log⁡3+13−1+π6