Carrying out a substituting to evaluate $\int (x + 1) (x^2 + 2 x)^5dx$ The problem is:
$$ \int { (x+1)({ x }^{ 2 } } +2x{ ) }^{ 5 }dx $$
The next step given by WolframAlpha is 
$$\int { (x+1)({ x }^{ 2 } } +2x{ ) }^{ 5 }dx\\ =\quad \frac { 1 }{ 2 } \int { { u }^{ 5 }du }  $$
(While I realize I am doing somthing worng)
The steps I am taking are : $ \int { (x+1)({ x }^{ 2 } } +2x{ ) }^{ 5 }dx$. 
Let $u={ x }^{ 2 }+2x, \, du = 2x+2\, dx$. Then I see I can rewrite $du$ as $du = 2(x+1)dx$ giving me $\frac { du }{ 2 } = (x+1)\, dx$.
I can now see where the $ \frac { 1 }{ 2 }  $ is coming from, but I cannot seem to visualize the next steps to get to
$$ \int { (x+1)({ x }^{ 2 } } +2x{ ) }^{ 5 }dx=\frac { 1 }{ 2 } \int { { u }^{ 5 }du }  $$

Since $(x^2 + 2 x)^5 = u^5$, we can use the equation $(x + 1) \,dx = \frac{1}{2} du$ to write the integral as
$$\int \underbrace{(x^2 + 2 x)^5}_{u^5} \,\underbrace{(x + 1) \,dx}_{\frac{1}{2} du} = \int u^5 \cdot \frac{1}{2} du = \frac{1}{2} \int u^5 \,du .$$
