anonymous
  • anonymous
what is a integral of x multiple the square of 2x+1 dx?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
integral x(2x+1)^2 =integral x(4x^2+4x+1) =integral (4x^3 + 4x^2 +4x) =x^4 + (4/3)x^3 +2x^2 +C, where C is a constant
anonymous
  • anonymous
=integral (4x^3 + 4x^2 +x) =x^4 + (4/3)x^3 +(1./2)x^2 +C, where C is a constant
anonymous
  • anonymous
the last two steps are wrong. This should be correct

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anonymous
  • anonymous
sorry I met the square root not the square i.e. the integral x(2x+1)^0.5 dx
anonymous
  • anonymous
integral x(2x+1)^0.5 dx =integral (1/2)(2x+1)^(1/2) d(2x+1) =(1/2)(2/3)(2x+1)^(3/2) =(1/3)(2x+1)^(3/2) +C
anonymous
  • anonymous
why do u put 1/2 in x?
anonymous
  • anonymous
in step 2
anonymous
  • anonymous
because it replace dx to d(2x+1)which is equal to 2xdx. Comparing this to the original one, We have to cancel the extra 2 so multiply it by 1/2

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