What is the integral of ln(1+2^t) ?

The integral of ln(1+2^t) is -(\Li_{2}(-2^t))/(ln(2))+C

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integral of ln(1+2^t)

\int ln (1 + 2^{t}) d t

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

Solution steps

\int ln (1 + 2^{t}) d t

Use the nonelementary integral:

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

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

Add a constant to the solution

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

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