Id highly appreciate it if anyone could help me with any of the following

problems!

What is the antiderivative of (cosx)^4 (cos(x^4))??

Find lim as x->infinity [(2x-3)/(2x+5)]^2x+1

Find lim as x->infinity [e^(x^2) - e^ [(x^2) + xsinx)] ]

Find f ' (x) and f '' (x) if f(x)= e^(-1/sin^2x) ,where x is between negative pi/2 and positive pi/2

f(x)= 0 , where x = 0

Thanks in advance!