Question

integrate sqrt(e^x) dx

Answer 1

sqrt(e^x) dx=e^{x/2} Got the idea?

Answer 2

why not apply index laws and make it

\[\int\limits e^{\frac{1}{2} x} dx\]

Answer 3

@campbell_st then ?

Answer 4

well isn't it

\[\int\limits e^{\frac{x}{2}} dx = 2e^\frac{x}{2} + C\]

you can differentiate to check

Answer 5

thanks @campbell_st

Answer 6

Put e^x = u
then e^x dx = du
dx = (1/u) du

Answer 7

Another possible substitution, \(y=\sqrt e^x\), so \(y^2=e^x\) and \(dy=\dfrac{e^x}{2\sqrt e^x}~dx\), which gives the same outcome as @midhun.madhu1987's suggestion.