Question

∫√3+2xdx

Answer 1

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

Answer 2

\[\sqrt{3+2x}\] ?

Answer 3

yes

Answer 4

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

Answer 5

ok

Answer 6

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

Answer 7

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

Answer 8

ok

Answer 9

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.

Answer 10

So your final answer should be [2u^(3/2)]/3

Answer 11

ok

Answer 12

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

Answer 13

ok

Answer 14

Any other questions?

Answer 15

yes

Answer 16

Ok what?

Answer 17

∫x+1/2x-x2+2 dx

Answer 18

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

Answer 19

tthanks God bless you