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X log 2x

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X log 2x

Posted by Baba Tushir 2 years, 4 months ago

CBSE > Class 12 > Mathematics

1 answers

Preeti Dabral 2 years, 4 months ago

$\int {x\log 2xdx}$

$= \int {\left( {\log 2x} \right)xdx}$

$= \left( {\log 2x} \right)\int {xdx - \int {\left[ {\frac{d}{{dx}}\log 2x\int {xdx} } \right]dx} }$

[Applying product rule]

$= \left( {\log 2x} \right)\frac{{{x^2}}}{2} - \int {\frac{1}{{2x}}.2.\frac{{{x^2}}}{2}dx}$

$= \frac{1}{2}{x^2}\log 2x - \frac{1}{2}\int {xdx}$

$= \frac{1}{2}{x^2}\log 2x - \frac{1}{2}\frac{{{x^2}}}{2} + c$

$= \frac{{{x^2}}}{2}\log 2x - \frac{{{x^2}}}{4} + c$

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