Question

∫((6x+3)/(x^2 + x)) dx

All work is greatly appreciated

Answer 1

3(log(x)+log(x+1) + c

Answer 2

oh no, the entire solution disapeared

Answer 3

It was wrong, sorry. When I replaced dx in the integral I accidentally used du.

Answer 4

oh, okay thanks! You really understand these concepts well

Answer 5

Here is a correct solution:
\[ u=3(x^2+x) \\
du=(6x+3)dx \]
and
\[ \int{\frac{6x+3}{x^2+x}dx} = \int{\frac{du}{u/3}} = 3\int{\frac{du}{u}} = 3\ln{u}+C \]
Substituting back u gives:
\[ 3\ln{3(x^2+x)}+C = 3\ln(3x(x+1))+C = 3(\ln(3x)+\ln(x+1))+C \]

Answer 6

But ln(3x) is just ln(3)+ln(x) and ln(3) can be included in the constant. So kryptons solution is equivalent.