Question

\[\int\limits_{1}^{2}1/(x(x+1)) dx\]

Answer 1

You can transform the integrand: \[\frac{1}{x(x+1)} = \frac{1}{x} - \frac{1}{x+1}\]

Answer 2

\[\int\limits_{1}^{2}dx/x-\int\limits_{1}^{2}dx/(x+1)=\ln(x/(x+1))|_{1}^{2}=\ln(1/2)-\ln(2/3)\]

Answer 3

ln(1/2)-ln(2/3)=ln(3/4)

Answer 4

Shouldn't it be the other way around?
\[\ln(2/3) - \ln(1/2) = \ln(4/3)\]

Answer 5

Yh I got ln(4/3) too

Answer 6

yes i did a mistake with a minus