Question 8 - A-Level Maths

8. (a) Integrate

$\quad \mathrm { e } ^ { - 3 x + 5 }$
$x ^ { 2 } \ln x$
(b) Use an appropriate substitution to show that $$\int _ { 0 } ^ { \frac { 1 } { 2 } } \frac { x ^ { 2 } } { \sqrt { 1 - x ^ { 2 } } } \mathrm {~d} x = \frac { \pi } { 12 } - \frac { \sqrt { 3 } } { 8 }$$