Mathematics

# Solve $\int { (\log_ e x)^2} dx$ o

$x[(\log x)^2 - 2(\log x)+2] + c$

##### SOLUTION
$\displaystyle I=\int (\log x)^{2}dx$
Let $u=(\log (x))^{2}$         $du=\dfrac{210gx}{x}dx$
$dv=dx$             $v=x$
Now $\displaystyle \int \log x dx = x \log |x|-x+c$
$\therefore \displaystyle \int (\log x dx)^{2}dx=\int udv$
$\displaystyle =uv-\int udv$
$=\displaystyle x(\log |x|)^{2}-\int 2 \log x dx$
$=x(\log |x|)^{2}-2(x \log |x|-x)+c$
$=x(\log |x|)^{2}-2x \log |x|+2x+c$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

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