Board index Computation of Integrals Double integral of Logarithm

## Double integral of Logarithm

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### Double integral of Logarithm

Tue Oct 04, 2016 2:01 pm

Posts: 105
How to obtain the closed form of the following integral
$\int\limits_0^1 {\int\limits_0^x {\frac{{{{\ln }^k}\left( {1 - t} \right){{\ln }^m}\left( {1+x} \right)}}{{\left( {1 + t} \right)\left( {1 - x} \right)}}dtdx} } = ?$
where $k$ and $m$ are positve integers.

### Re: Double integral of Logarithm

Thu Oct 06, 2016 11:46 am

Posts: 22

### Re: Double integral of Logarithm

Thu Oct 06, 2016 12:59 pm

Posts: 105

x is Integral variable. $\int\limits_0^1 {\int\limits_0^x {\frac{{{{\ln }^k}\left( {1 - t} \right){{\ln }^m}\left( {1 + x} \right)}}{{\left( {1 + t} \right)\left( {1 - x} \right)}}dtdx} } = \int\limits_0^1 {\frac{{{{\ln }^m}\left( {1 + x} \right)}}{{1 - x}}\int\limits_0^x {\frac{{{{\ln }^k}\left( {1 - t} \right)}}{{1 + t}}dtdx} }$