Evaluate: ∫ 1 / (sin⁴ x + cos⁴ x) dx

Evaluate: ∫ 1 / (sin⁴ x + cos⁴ x) dx

• A. (1/√2) tan⁻¹((tan² x - 1) / (√2 tan x)) + C
• B. (1/√2) tan⁻¹(√2 tan x) + C
• C. tan⁻¹(tan² x) + C
• D. log|sin⁴ x + cos⁴ x| + C

Answer: A) (1/√2) tan⁻¹((tan² x - 1) / (√2 tan x)) + C

Explanation: Divide by cos⁴ x to get sec² x dx / (tan⁴ x + 1). Put tan x = t. Then ∫ (t² + 1 - t²) / (t⁴ + 1) dt. Breaking and substituting u = t - 1/t gives the result.