(1) Integrate the following functions:
(a) I= ∫ (8³+10x¹ - 12x³)dx 2
(b) I= ∫ (1/x^3-2/x+14x^3/4)dx
(c) 1 = ∫ (15 sin(5x) - 2 cos(x/2)) dx
(d) 1 = ∫ (6e^2x + 12e^2x)dx
(2) Find the original function f(x) given f'(x) = 8x³ +10r4 - 12r5 and f(-1) = 7.
(3) Find the original function f(x) given f'(x) = 15 sin(5x) - 2 cos(x/2) and f(π) = 1.
(4) Find the original function f(x) given f'(x) = 10/x and f(e) = 1.