1. integral

how do you integrate √(2^x) i know this equals 2^.5x . i know the general integral formula a^x =(a^x) /ln a but when i apply that here i get 2^.5x /ln(2) which is not right. i am not sure what i am doing wrong

2. Re: integral

Try a u-substitution: $u=\tfrac{1}{2}x$

3. Re: integral

Check your work below. Better yet, check my work

$\sqrt{2^x}=(2^x)^{1/2} = 2^{\frac{1}{2}x}$

$u=\tfrac{1}{2}x$ and $du=\tfrac{1}{2}dx \implies dx = 2du$

$\int 2^{\frac{1}{2}x} dx = \int 2^u (2du) = \frac{2^u}{\ln(2)}\cdot 2 +c =\frac{2^{u+1}}{\ln(2)}+c= \frac{2^{\frac{1}{2}x+1}}{\ln(2)}+c$