Question

How to evaluate the integral `int s*2^s ds` ?

Answer 1

Refer to explanation

Explanation:

Using integration by parts we have

#int s*2^sds=int s*(2^s/log2)'ds=s*2^s/log2-1/log2int s' 2^s ds= s*2^s/log2-1/log2 int 2^s ds=(s*2^s)/log2-2^s/(log2)^2#

Finally

`int s*2^sds=2^s/(log2)^2*(slog2-1)+c`

where `c`=constant