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Integrate : $\int \log _a x dx$

$(a)\;\frac{x}{\log a } (\log x -1)+c \\(b)\;x \log (\log x -1)+c) +c \\(c)\; x \log x -x +c \\ (d)\;None\;of\; these $

1 Answer

<div class="clay6-step-odd"><div class="clay6-basic" id="pr10">$\int \log _a x dx$</div><div class="clay6-basic" id="pr11">=&gt; $\int \large\frac{\log _e x }{\log _e a }$$dx$</div><div class="clay6-basic" id="pr12">=&gt; $ \large\frac{1}{\log _e a }$$\int \log _e x dx$</div><div class="clay6-basic" id="pr13">=&gt; $\large\frac{1}{\log _e a} $$\bigg\{ \log _e x.x -\int \large\frac{1}{x}.$$xdx \bigg \}$</div><div class="clay6-basic" id="pr14">=&gt; $\large\frac{1}{\log a} $$\{ x \log _e x -x \}+c$</div><div class="clay6-basic" id="pr15">$\large\frac{x}{\log a } $$(\log x -1)+c$</div><div class="clay6-basic" id="pr16">Hence a is the correct answer. </div></div>
answered Dec 31, 2013 by meena.p