Question

Evaluate each indefnite integral using parts:
intf(x*2^-x)dx

Answer 1

\[\int\limits(x*2^-x) dx\]
u=x and dv=2^-x dx

Answer 2

I've gotten to this point
\[\int\limits(2^-x dx)=\left(\begin{matrix}2^-x \\ \ln2\end{matrix}\right)-\int\limits(1*2^-x)\]

Answer 3

\[\int x(2^{-x})dx\]Using LIPETs (or LIATE) to decide on my function of u: I have \[u = x~,~ du=dx~,~ dv=2^{-x}\]\[v=\int 2^{-x}dx = -\frac{2^{-x}}{\log(2)}=-\frac{1}{2^x\log(2)}\]Integration by parts states: \(\int udv = uv - \int vdu\)