What is the integral from 1 to 2 of ln(1+2^x) ?

The integral from 1 to 2 of ln(1+2^x) is (-\Li_{2}(-2^2)+\Li_{2}(-2))/(ln(2))

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integral from 1 to 2 of ln(1+2^x)

\int_{1}^{2} ln (1 + 2^{x}) d x

\frac{- Li _{2} ( - 2 ^{2} ) + Li _{2} ( - 2 )}{ln ( 2 )}

Solution steps

\int_{1}^{2} ln (1 + 2^{x}) d x

Use the nonelementary integral:

\int ln (1 + 2^{x}) d x = - \frac{Li _{2} ( - 2 ^{x} )}{ln ( 2 )}

= [- \frac{Li _{2} ( - 2 ^{x} )}{ln ( 2 )}]_{1}^{2}

Compute the boundaries:

\frac{- Li _{2} ( - 2 ^{2} ) + Li _{2} ( - 2 )}{ln ( 2 )}

= \frac{- Li _{2} ( - 2 ^{2} ) + Li _{2} ( - 2 )}{ln ( 2 )}

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What is the integral from 1 to 2 of ln(1+2^x) ?
The integral from 1 to 2 of ln(1+2^x) is (-\Li_{2}(-2^2)+\Li_{2}(-2))/(ln(2))