My full solutions:
1) 1/8 - 15/16 x + 75/16 x^2 - 625/32 x^3
2) 0.6595, 1.083, 8/3 ln(2) - 7/9
3) (-2-4xy)/(2x^2 + 4 + pisin(0.5pi)), (3pi+62)/(pi+22)
4) x=e^(ln(60)-2.5t)), 633 mins
5) (-5root(3)/16), (4,5root3)
6) 3ln(3y+2)-2ln(y)+c, lambda=8, 4pi/3 - root3
7) k=17/2, 1696pi/5
8) {3,5,0}, r = {1,5,2} + lambda{-5,4,3}, k=2, cos(theta)=4/5, area=12/5, possible positions {3, 33/5, 16/5} and {-1, 17/5, 4/5}