## anonymous 5 years ago ∫√3+2xdx

1. anonymous

Is 3+2x all under the square root or is it just root 3?

2. anonymous

$\sqrt{3+2x}$ ?

3. anonymous

yes

4. anonymous

Ok. We will use u-substitution. Set u equal to what's under the square root (3+2x) and then take the derivative of 3+2x to find du. So du = 2 dx

5. anonymous

ok

6. anonymous

So you are left with $\int\limits \sqrt{u}/2 du$

7. anonymous

The reason we divide by 2 is when you get du = 2 dx you want dx by itself, so you get du/2 = dx

8. anonymous

ok

9. anonymous

Since your dividing by 2, you can pull a 1/2 out in front of the integral, leaving you with the integral of root u, which can be rewritten as u^(1/2). Then to integrate we add 1 to the exponent (giving us u^(3/2)). We have to multiply by the reciprocal of our new exponent.

10. anonymous

11. anonymous

ok

12. anonymous

Since 2/3 times u^(3/2) just moves the u^(2/3) on top and multiplies it by 2.

13. anonymous

ok

14. anonymous

Any other questions?

15. anonymous

yes

16. anonymous

Ok what?

17. anonymous

∫x+1/2x-x2+2 dx

18. anonymous

Oh well I meant about this problem. I'll look at it and see if I can help in the other problem.

19. anonymous

tthanks God bless you