Question 5 - A-Level Maths

1. By writing $\ln x$ as $( \ln x ) \times 1$, use integration by parts to find $\int \ln x \mathrm {~d} x$.
2. Find $\int ( \ln x ) ^ { 2 } \mathrm {~d} x$.
Use the substitution $u = \sqrt { x }$ to find the exact value of $$\int _ { 1 } ^ { 4 } \frac { 1 } { x + \sqrt { x } } \mathrm {~d} x$$