Integrate by parts x2^x

Here we will use integration by parts because we have the product of two terms, x and 2^x. Using the integration by parts formula, we have to differentiate one of these terms and integrate the other. We choose to differentiate x, as this becomes 1, less complicated than before. We can then integrate 2^x without it becoming any more complicated, only changing by a factor of ln(2). Sticking these results into the formula gives us the answer for the question. 

See whiteboard.