What is the integral of s*2^s ?

The integral of s*2^s is (2^ss)/(ln(2))-(2^s)/(ln^2(2))+C

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integral of s*2^s

\int s \cdot 2^{s} d s

\frac{2 ^{s} s}{ln ( 2 )} - \frac{2 ^{s}}{ln ^{2} ( 2 )} + C

Solution steps

\int s \cdot 2^{s} d s

Apply Integration By Parts

: \frac{2 ^{s} s}{ln ( 2 )} - \int \frac{2 ^{s}}{ln ( 2 )} d s

= \frac{2 ^{s} s}{ln ( 2 )} - \int \frac{2 ^{s}}{ln ( 2 )} d s

\int \frac{2 ^{s}}{ln ( 2 )} d s = \frac{2 ^{s}}{ln ^{2} ( 2 )}

= \frac{2 ^{s} s}{ln ( 2 )} - \frac{2 ^{s}}{ln ^{2} ( 2 )}

Add a constant to the solution

= \frac{2 ^{s} s}{ln ( 2 )} - \frac{2 ^{s}}{ln ^{2} ( 2 )} + C

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What is the integral of s*2^s ?
The integral of s*2^s is (2^ss)/(ln(2))-(2^s)/(ln^2(2))+C