Question

Evaluate the following integral : ∫1/(sin⁴x+sin²x cos²x+cos⁴x)dx

\(\int\frac{1}{sin^4x+sin^2x\,cos^2x+cos^4x}\)dx

Answer 1

Given,

∫1/(sin⁴x+sin²x cos²x+cos⁴x)dx

Multiplying sec⁴x in both numerator and denominator,

Assume,

tan x = t 

sec²xdx = dt