Need help

i read the question ( given below) but couldn't understand the answer \[\large\int _{ 0 }^{ 1 }{ (\left( \prod _{ N=1 }^{ S }{ \left( x+N \right) } \right) (\sum _{ D=1 }^{ S }{ \frac { 1 }{ (x+D) } ) } )dx }\] in the answer it was asked to assume (x+1)(x+2)........(x+s)=e^t such take we can take log both sides and differentiate such that \[\large\sum _{ D=1 }^{ S }{ \frac { 1 }{ (x+D) } ) } )dx = dt\] but how is this assumption (x+1)(x+2)........(x+s)=e^t possible ????

#Calculus

Easy Math Editor

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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$