Mathematics

# $\int\frac{dx}{x(x^n+1)}$

$\frac{1}{n}$ $(log{x^n}$-$log(x^n +1))+C$

##### SOLUTION

$\\I=\int (\frac{1}{x(x^n+1)})dx\\I=\int (\frac{1}{x^n(x^n+1)})dx\\let x^n=t then nx^{n-1}dx=dt \\\therefore I=(\frac{1}{n})\int (\frac{1}{t(t+1)})dx\\=(\frac{1}{n})\int ((\frac{1}{t})-(\frac{1}{t+1}))dx\\ =(\frac{1}{n})[logt-log(t+1)]+c\\=(\frac{1}{n})[logx^n-log(x^n+1)]+c$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

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