Question 10 - A-Level Maths

Exam Board	AQA
Module	C3 (Core Mathematics 3)
Year	2013
Session	June
Topic	Integration by Substitution

1. By writing $\ln x$ as $( \ln x ) \times 1$, use integration by parts to find $\int \ln x \mathrm {~d} x$.
2. Find $\int ( \ln x ) ^ { 2 } \mathrm {~d} x$.
  (4 marks)
Use the substitution $u = \sqrt { x }$ to find the exact value of $$\int _ { 1 } ^ { 4 } \frac { 1 } { x + \sqrt { x } } \mathrm {~d} x$$ (7 marks)