Integration of ln(x) alone

A question is this type if and only if it asks to integrate ln(x) or ln(ax+b) by itself, typically using integration by parts with u=ln(x) and dv=dx.

2 questions · Standard +0.3

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OCR MEI C3 Q6

6 marks Standard +0.3

6 Find \(\frac { \mathrm { d } } { \mathrm { d } x } ( x \ln x )\) and hence or otherwise find the value of \(\int _ { 2 } ^ { 3 } \ln x \mathrm {~d} x\), giving your answer in the form \(\ln a + b\), where \(a\) and \(b\) are to be determined.

OCR C4 2012 June Q2

5 marks Standard +0.3

2 Use integration by parts to find \(\int \ln ( x + 2 ) \mathrm { d } x\).