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

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

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integral of ln(1+2^x)

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

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

Solution steps

\int 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 )}

Add a constant to the solution

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

\int_{1}^{3} r^{3} ln (r) d r

\frac{d}{d x} (\frac{2 ^{2} - x ^{2}}{2})

7 x^{2} - x^{3}

(x - 2) (4 x + 2)

4^{s i n^{2} (x) + c o s (3 x)}

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