(b) Find (b) \( L \frac{\sin 5 t}{t} \)

\( \int \frac { x \ln x - x } { \ln ^ { 3 } x } \)

The rate at which an object changes temperature, \( \frac{d T}{d t} \) is proportional to the difference between its temperature, \( T \) and the temperature of the surrounding medium, \( T_{s} \) - \( \frac{d T}{d t}=k\left(T_{s}-T\right) \) (a) Solve the differential equation for \( T(t) \)

Given the functions \( f(x) = x^{\frac{1}{3}} \) and \( g(x) = x^{3} \), show that they are inverses by calculating their compositions \( f(g(x)) \) and \( g(f(x)) \).

3) A particle moving on a straight line with acceleration \( a(t)=6 t-6 \). After 4 secs, its velocity was \( 30 \mathrm{~m} / \mathrm{s} \) and had covered a distance of 60 m . Determine the expression in terms of time for \( \begin{array}{ll}\text { i) } \quad \text { its velocity } & \text { ii) its distance }\end{array} \)

seconds, is given by \( a(t)=t+1 \). Given that \( s=0 \) and \( v=8 \) when \( t=0 \), find formula for: (a) The velocity \( v \) (b) The displacement