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1 ? 0 (x n - 1) / ln ( x ) What is the value of this integral please help??

1 ? 0(xn-1) /ln(x) 
 
What is the value of this integral please help??

Grade:12

2 Answers

jagdish singh singh
173 Points
5 years ago
\hspace{-0.7 cm.}$Let $I = \int_{0}^{1}\frac{x^n-1}{\ln x}dx = \int_{0}^{1}\left(\int_{0}^{n}x^tdt\right)dx = \int_{0}^{n}\left(\int_{0}^{1}x^tdx\right)dt$\\\\\\So we get $I =\int_{0}^{n}\left[\frac{x^{n+1}}{n+1}\right]_{0}^{1}dt= \int_{0}^{n}\frac{1}{t+1}dt = \ln|n+1|$
jagdish singh singh
173 Points
5 years ago
 
$Sorry i second line , It is $I=\int_{0}^{n}\left[\frac{x^{n+1}}{t+1}\right]_{0}^{1}dt$

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