∫ logx dx=∫ logx 1 dx Use ILATE rule and integrate considering logx as first function amp; 1 as second function, we get I= logx (∫ 1 dx) ∫ (1x)(∫ 1 ...

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Byju's Answer

Standard XII

Mathematics

Chain Rule of Differentiation

Find ∫log x...

Question

Find $\int log x d x$

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Solution

$\int l o g x d x = \int l o g x 1 d x$
Use ILATE rule and integrate considering logx as first function & 1 as second function, we get
$I = l o g x (\int 1 d x) - \int (\frac{1}{x}) (\int 1 d x) d x$
$= x l o g x - \int (\frac{1}{x}) x d x$
$= x l o g x - x + C$

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Find ∫logxdx

∫logxdx=∫logx1dxUse ILATE rule and integrate considering logx as first function & 1 as second function, we getI=logx(∫1dx)−∫(1x)(∫1dx)dx=xlogx−∫(1x)xdx=xlogx−x+C

Find $\int log x d x$

$\int l o g x d x = \int l o g x 1 d x$
Use ILATE rule and integrate considering logx as first function & 1 as second function, we get
$I = l o g x (\int 1 d x) - \int (\frac{1}{x}) (\int 1 d x) d x$
$= x l o g x - \int (\frac{1}{x}) x d x$
$= x l o g x - x + C$