1. ## Substitution Method Help

The substitution $\displaystyle u=2x+7$ transforms the "x"-integral
$\displaystyle \displaystyle \int \frac{4 x + 3}{\sqrt{2 x + 7}} \ dx$
into the "u"-integral

ok, so I can rewrite this as:

$\displaystyle \displaystyle \int (4 x + 3)(2 x + 7)^{\frac{-1}{2}} \ dx$
$\displaystyle u=2x+7$
$\displaystyle du=2dx$
I can't figure out how to force this to equal 4x+3

All I can do is
$\displaystyle 2\int u^{\frac{-1}{2}}*du$

which will give me my 4, but I'm still missing the x+3 part!

What am I missing?

2. Originally Posted by Vamz
The substitution $\displaystyle u=2x+7$ transforms the "x"-integral
$\displaystyle \displaystyle \int \frac{4 x + 3}{\sqrt{2 x + 7}} \ dx$
into the "u"-integral

ok, so I can rewrite this as:

$\displaystyle \displaystyle \int (4 x + 3)(2 x + 7)^{\frac{-1}{2}} \ dx$
$\displaystyle u=2x+7$
$\displaystyle du=2dx$
I can't figure out how to force this to equal 4x+3

All I can do is
$\displaystyle 2\int u^{\frac{-1}{2}}*du$

which will give me my 4, but I'm still missing the x+3 part!

What am I missing?
Dear Vamz,

$\displaystyle \displaystyle \int \frac{4 x + 3}{\sqrt{2 x + 7}} \ dx$

$\displaystyle u=2x+7\Rightarrow{dx=\frac{du}{2}}$

Also, $\displaystyle x=\frac{u-7}{2}$

Substituting these in the above integration;

$\displaystyle \displaystyle \int \frac{4 \left(\frac{u-7}{2}\right) + 3}{2\sqrt{u}} \ du$

$\displaystyle \displaystyle\frac{1}{2}\int \frac{2u-11}{\sqrt{u}}du$

Hope you can continue.