The value of the integral ∫ 1 2 + 1 x 2 - 1 x 2 + 1 1 1 + x 4 d x is

Step-by-step solution

∫ 1 2 + 1 x 2 - 1 x x + 1 x x x 2 + 1 x 2 d x = ∫ 1 2 + 1 1 - 1 x 2 x + 1 x x + 1 x 2 - 2 d x Let x + 1 x = 2 sec θ 1 - 1 x 2 d x = 2 sec θ tan θ d θ ∫ π / 4 π / 3 2 sec θ tan θ d θ 2 sec θ 2 tan θ = π 12 2