Integration using substitution

[Dro]

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 that's wrong. please help!

 

[Mark44]

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.

 

[Dro]

wouldnt it be easier to substitute another letter like w for 1+u instead? although this did not give me the right number. i don't really get how to divide u by (1+u)

 

[Mark44]

You could use substitution again, but it's probably quicker to just carry out the division. See http://en.wikipedia.org/wiki/Polynomial_division

u/(u + 1) = 1 + -1/(u + 1)

 

[Mark44]

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.

 

[Dro]

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