Evaluate the integral ∫(x/√(5-4x2-x4))dx

Question

Evaluate the integral ∫(x/√(5-4x²-x⁴))dx. Please show all steps.

Answer 1

I = ∫(x/√(5-4x²-x⁴))dx = ∫x/√[9 - (x²+ 2)²]. Let do subctitution: x² + 2 = 3sinu; 2xdx = 3cosudu;

I = 3/2∫cosu/3cosudu = 2/9u + C = 2/9sin^-1[(x² + 2)/3] + C