Integration by Substitution I have the following problem: $\int (x+2)(2x-3)^6dx$
What I did was allow $u = 2x-3$
$dx= \frac{1}{2}du$
Since I am integrating w.r.t u I decided to let $x=\frac{u+3}{2}$
my new equation is $\int ( \frac{u+3}{2}+2)(u^6)\frac{1}{2}du$
which I then simplify to $\int ( \frac{u+7}{4})(u^6)du$
I think I did something wrong because my following steps aren't giving the correct answer 

simplifying your Integrand we get $$\frac{1}{4}\int (u+7)u^6du$$ further we get the integral $$\frac{1}{4}\int\left( u^7+7u^6\right)du$$
