# U-substitution problem

1. Jun 24, 2015

### RyanTAsher

1. The problem statement, all variables and given/known data
Evaluate the integral using usub

int(x*sqrt(1+x)dx) from 0 to 8
2. Relevant equations

3. The attempt at a solution
Okay, so I attempted to set for u sub

U = x+1
u^2 = (x+1)^2
2u*du = 2(x+1)*dx
u*du -1 = x*dx

I got this far but I don't understand what to do with this, because of the (-1), separate from the u*du

2. Jun 24, 2015

### RUber

There is no reason to square u.
Just take the derivatives, du = dx, x = u-1. Then you have a normal polynomial in u.

3. Jun 26, 2015

### LCKurtz

Slight nit-pick -- it isn't actually a polynomial though it does only have terms of the form $x^p$.

4. Jun 26, 2015

### Ray Vickson

In the "Geometric Programming" literature, it would be called a "signomial". (It would further be called a "posynomial" if all its coefficients were $>0$.)

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