∫ ( tan^2 x + tan^4 x )dx

∫ ( tan²x + tan⁴x) dx
= ∫ tan²x (1 + tan²x) dx
= ∫ tan²x sec²x dx
= ∫ tan²x d tanx
= (1/3) tan³x + c

∫ ( tan^2 x + tan^4 x )dx
=∫ ((secx)^2-1 +((secx)^2-1) ^2 )dx
=∫ ( (secx)^2-1+(secx)^4-2*(secx)^2+1)dx
=∫ ((secx)^4-( secx)^2)dx
∫( ( secx)^2-1)dtanx
=∫ ( tanx )^2dtanx
=1/3*(tanx)^3+c