∫_0 ^(tan^(−1) (((2×1(5(√2)−1))/( 5(√2)(5(√2)−2))))) 2(1+(√(1^2 −((5−1)(√2)tan α−1)^2 ))cot (((((3π)/4)−sin^(−1) (((√(1^2 −((5−1)(√2)tan α−1)^2 ))/( (√2)(5−1)))))/2))−(1−(√(1^2 −((5−1)(√2)tan α−1)^2 )))tan ((π/4)−sin^(−1) (((√(1^2 −((5−1)(√2)tan α−1)^2 ))/( (√2)(5−1))))))((5(√2))/(cos^2 α))dα