U-Substitution Problem

**Audioslavery** · April 17th 2010, 11:46 PM

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

Any advice?

**harish21** · April 18th 2010, 12:02 AM

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

Any advice?

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

substitute this in your integral to get:

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

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

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

rewrite

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

and integrate

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