Please help me evaluate
e^(x)^1/2/ (x^1/2)
I started out with u substitution. First I let radical x be u, but I couldn't work it out properly because I didn't know what to cross out. Please give me some insight on this!
Exactly. Unfortunately, there isn't a 1/2 inside the integral, so you can't substitute $\displaystyle du = \frac{1}{2\sqrt{x}}dx$ yet. Fortunately, you can place a 1/2 inside the integral as long as you place a 2 outside the integral (to balance the 1/2). Now, the problem looks like:
$\displaystyle 2\int \frac{e^{\sqrt{x}}}{2\sqrt{x}} \, dx$
Substituting $\displaystyle u = \sqrt{x}$ and $\displaystyle du = \frac{1}{2\sqrt{x}}dx$ gives:
$\displaystyle 2\int e^u \, du$
Strictly speaking, what you wrote here was
$\displaystyle \frac{\left(e^x)^{1/2}}{x^{1/2}}= \frac{e^{\frac{x}{2}}}{x^{1/2}}$
but apparently you meant
$\displaystyle e^{x^{1/2}}}{x^{1/2}}$
which would be e^(x^(1/2))/x^(1/2)
I started out with u substitution. First I let radical x be u, but I couldn't work it out properly because I didn't know what to cross out. Please give me some insight on this!