Find the integrals of the functions.

tan⁴x = tan²x.tan²x

= (sec²x-1) tan²x

= sec²x tan²x- tan²x

= sec²x tan²x- (sec²x-1)

= sec²x tan²x- sec²x+1

Now,

⇒

Now, let tanx = t

=> sec²x dx =dt

⇒

⇒