Improper integrals with infinite upper limit (combined rational terms)

Evaluate an improper integral with an infinite upper limit where the integrand is a combination of rational-type terms (e.g., differences of fractions like 1/x - 4/(4x+1) or 2x/(x²+4) - 4/(2x+3)), requiring careful limiting process to handle indeterminate forms.

2 questions · Challenging +1.0

4.08c Improper integrals: infinite limits or discontinuous integrands

Sort by: Default | Easiest first | Hardest first

AQA FP3 2009 June Q4

5 marks Standard +0.8

4 Evaluate the improper integral $$\int _ { 1 } ^ { \infty } \left( \frac { 1 } { x } - \frac { 4 } { 4 x + 1 } \right) \mathrm { d } x$$ showing the limiting process used and giving your answer in the form \(\ln k\), where \(k\) is a constant to be found.

AQA FP3 2013 June Q4

6 marks Challenging +1.2

4 Evaluate the improper integral $$\int _ { 0 } ^ { \infty } \left( \frac { 2 x } { x ^ { 2 } + 4 } - \frac { 4 } { 2 x + 3 } \right) \mathrm { d } x$$ showing the limiting process used and giving your answer in the form \(\ln k\), where \(k\) is a constant.