Integral Evaluation Using u-Substitution: x*sqrt(1+x)dx from 0 to 8

[Destroxia]

Homework Statement

Evaluate the integral using usub

int(x*sqrt(1+x)dx) from 0 to 8

Homework Equations

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

 

[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.

 

[LCKurtz]

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

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

 

[Ray Vickson]

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

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