## anonymous 5 years ago FInd the indefinite integral using substitution. let u = 2x^2 + 3x + 9. (4x + 3)/ (2x^2 + 3x + 9)^(7/3)dx. can someone please give me the steps and answer . im in desperate need

1. anonymous

du = (7/3)*(4x+3)^(4/3)

2. anonymous

Do you see that?

3. anonymous

Actually I take that back. Try [(7/3)(2x^2+3x+9)^(4/3)] * (4x+3) dx

4. anonymous

= du

5. anonymous

I got (-3/4)[(2x^2)+3x+9)^(-3/4)]+C

6. anonymous

Oh wait sorry. It's gettin close to bed time lol. Just ignore me. good grief

7. anonymous

you just have to take the derivative of 2x^2+3x+9 and you get du=4x+3 dx...then you can substitute for the numberator of the integrand...then you can take the integral and back substitute u=2x^2+3x+9 after that.

8. anonymous

numerator*

9. anonymous

$\int\limits_{?}^{?}( u^(-7/3) du$

10. anonymous

you can then take the integral of that

11. anonymous

and then back substitute u to get the answer