\( \int \frac { d x } { \sin x \cos ^ { 3 } x } = \)

5) A particle is moving in a straight line with velocity \( v(t)=15 t^{2}+2 \). Find; a) Its acceleration after 3 seconds b) Its displacement after 2 secnds

\( = \int _ { 0 } \frac { \partial t } { 1 + t ^ { 3 } } \)

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 \( \begin{array}{ll}\text { i) } \quad \text { its velocity } & \text { ii) its distance }\end{array} \)

\( F ( x ) = \int _ { 0 } ^ { \sin x } \frac { d t } { 1 + t ^ { 3 } } \)