help

[jeca86]

first make a substitution and then use integration by parts to evaluate the integral.

the integral has a 4 at the top and 1 at the bottom. the rest is e^(square root of x) * dx

so:

u=e^square root of x
dx=2du/u

im not sure what i have so far is right. can i get a walk through?

 

[Unco]

You could write it as \(\displaystyle \L\mbox{\int^4_1 \frac{e^{\left(\sqrt{x}\right)}}{\sqrt{x}} \cdot \sqrt{x} dx}\) and, by parts, let \(\displaystyle \L\mbox{u = \sqrt{x}}\) and \(\displaystyle \L\mbox{\frac{dv}{dx} = \frac{e^{\sqrt{x}}}{\sqrt{x}}}\).

Note that a u-substitution of \(\displaystyle \mbox{u=\sqrt{x}}\) may help you to integrate \(\displaystyle \L\mbox{\frac{e^{\left(\sqrt{x}\right)}}{\sqrt{x}}}\).