calculus antiderivative

Question

Find the particular antiderivative that satisfies the following conditions: 

dy/dx=6x^-2+8x^-1-3; y(1)=2

Answer 1

dy/dx = 6/x² + 8/x - 3

y = -6/x + 8 lnx - 3x + c

2 = -6 + 8 ln(1) - 3 + c

2 = -9 + c

c = 11

y = -6/x + 8 lnx - 3x + 11