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Integration using substitution

  • Thread starter Dro
  • Start date
  • #1
Dro
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Homework Statement


Integrate: 6/(1+sqrt(7x))dx


Homework Equations



the hint was that u^2=7x

The Attempt at a Solution


by substituting u, i got the antiderivative of (12/7)(u/(1+u))du so i substituted again and ended up getting 12/7(1+sqrt(7x)-ln(sqrt(7x)+1)) but apparently thats wrong. please help!
 
Last edited:

Answers and Replies

  • #2
33,162
4,847
Assuming that your work is correct in getting to an integrand of (12/7) u/(1 + u) * du, divide u by 1 + u using polynomial long division.
 
  • #3
Dro
7
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wouldnt it be easier to substitute another letter like w for 1+u instead? although this did not give me the right number. i dont really get how to divide u by (1+u)
 
  • #4
33,162
4,847
  • #5
33,162
4,847
Actually, I don't see anything wrong with your answer: 12/7(1+sqrt(7x)-ln(sqrt(7x)+1))
except that it is missing the constant of integration.
I get 12/7(sqrt(7x)-ln(sqrt(7x)+1)) + C, which differs from yours by a constant.
 
  • #6
Dro
7
0
thank you very much! i actually can't put the +C because i have to put it in online but i changed my answer to what you had which differed from mine by the +1 i had and it said I as correct
 

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