1. ## U-Substitution Problem

Sorry about the multitude of questions but I have a midterm on thursday! Woe is me! xD

This U-Sub has caused me some problems, I'm not quite sure how to approach it.

∫xdx/(1+√x)

If I substitute U=1+√x I get 1/2√x so that doesn't help
and if I substitute U=x that of course turns into du=dx

2. Originally Posted by Audioslavery
Sorry about the multitude of questions but I have a midterm on thursday! Woe is me! xD

This U-Sub has caused me some problems, I'm not quite sure how to approach it.

∫xdx/(1+√x)

If I substitute U=1+√x I get 1/2√x so that doesn't help
and if I substitute U=x that of course turns into du=dx

Let $\displaystyle u = \sqrt x$, then $\displaystyle du = \frac{1}{2 \sqrt x}dx \implies dx = du . 2 \sqrt x$

substitute this in your integral to get:

$\displaystyle \int x \times 2 \sqrt x \frac{1}{1+u} du$

$\displaystyle = 2 \int \sqrt x \times \sqrt x \times \sqrt x \frac{1}{1+u} du$

$\displaystyle = 2 \int \frac{u^3}{1+u} du$

rewrite

$\displaystyle \frac{u^3}{1+u} = u^2 - u + 1 - \frac{1}{1+u}$

and integrate