pls solve this integration ques

write sec⁴x as (1 + tan²x)²   now Let  tanx = t² ====> sec²x dx = 2t dt   ====> (1 + tan²x) dx = 2t dt                  ====> dx = 2t dt / (1 + t⁴)         putting this into above expression we get     (1 + t⁴)² 2t dt / t (1 + t⁴)     which is same as  2 (1 + t⁴) dt  =  2  1+ t⁴ dt   =  t / 2 + 2 t⁵ / 5

so   sec⁴x  ÷   tanx       dx  =  tanx / 2 + 2 tan^5/2x  / 5