Explain why \(\int _ { 1 } ^ { \infty } \frac { 1 } { x ( 2 x + 5 ) } \mathrm { d } x\) is an improper integral.
Prove that
$$\int _ { 1 } ^ { \infty } \frac { 1 } { x ( 2 x + 5 ) } \mathrm { d } x = a \ln b$$
where \(a\) and \(b\) are rational numbers to be determined. [0pt]
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