anonymous
  • anonymous
∫√3+2xdx
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
Is 3+2x all under the square root or is it just root 3?
anonymous
  • anonymous
\[\sqrt{3+2x}\] ?
anonymous
  • anonymous
yes

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anonymous
  • 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
anonymous
  • anonymous
ok
anonymous
  • anonymous
So you are left with \[\int\limits \sqrt{u}/2 du\]
anonymous
  • 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
anonymous
  • anonymous
ok
anonymous
  • 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.
anonymous
  • anonymous
So your final answer should be [2u^(3/2)]/3
anonymous
  • anonymous
ok
anonymous
  • anonymous
Since 2/3 times u^(3/2) just moves the u^(2/3) on top and multiplies it by 2.
anonymous
  • anonymous
ok
anonymous
  • anonymous
Any other questions?
anonymous
  • anonymous
yes
anonymous
  • anonymous
Ok what?
anonymous
  • anonymous
∫x+1/2x-x2+2 dx
anonymous
  • anonymous
Oh well I meant about this problem. I'll look at it and see if I can help in the other problem.
anonymous
  • anonymous
tthanks God bless you

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