If \(\begin{vmatrix}  1+2x & -1 \\ 6 & 3-x \end{vmatrix} = -3 \), find the values of x.

Find \(\int \frac{x^{3} + 5x + 1}{x^{3}} \mathrm {d} x\)

Find the coordinates of the point which divides the line joining P(-2, 3) and Q(4, 6) internally in the ratio 2 : 3.

A particle starts from rest and moves in a straight line such that its acceleration after t seconds is given by \(a = (3t - 2) ms^{-2}\). Find the other time when the velocity would be zero.

A particle starts from rest and moves in a straight line such that its acceleration after t secs is given by \(a = (3t - 2) ms^{-2}\). Find the distance covered after 3 secs.