## anonymous 4 years ago if du/dx=2x+6 what does du equal? this is using substitution for solving an indefinite integral.

1. anonymous

i guess $du=(2x+6)dx$ what is the actual problem?

2. anonymous

du = (2x + 6)dx You can now integrate both sides to solve for u

3. anonymous

$u = x^2 + 6x + C$

4. anonymous

$\int\limits_{?}^{?} x+3/(x^2+6x)^2 dx$

5. anonymous

oh ok $u=x^2+6x$ $du= (2x+6)dx$ $\frac{1}{2}du=(x+3)dx$ and then you get $\frac{1}{2}\int \frac{1}{u}du$

6. anonymous

a set up for a u - sub. then anti derivative is $\frac{1}{2}\ln(u)$ , replace u by $x^2+6x$ and you are done

7. anonymous

omg thank you sooooo much!!!