Answer
$c$=$\frac{1}{e-1}$
Work Step by Step
$\int^{c+1}_c\frac{1}{x}dx$
=$\ln(c+1)-\ln c$
=$\ln(\frac{c+1}{c})$
Solving
=$\ln(\frac{c+1}{c})$=$1$
we find,
$\frac{c+1}{c}$=$e$
and thus
$c$=$\frac{1}{e-1}$
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