Question

how to integrate (6x+7) dx / (x+2)^2

Answer 1

You can do partial fractions for this, do you know how to do this?

Answer 2

i know.. i will try to use partial fractions

Answer 3

Write 6x+7 as 3*(x+2)+1
so it reduces to 3/(x+2) + 1/(x+2)^2

Answer 4

\[\int\limits\frac{6}{(x+2)} +\int\limits \frac{-5}{(x+2)^{2}} \]
\[\int\limits\frac{6}{(x+2)} \] \[6\int\limits\frac{1}{x+2} = 6\ln(x+2)\]
\[\int\limits\frac{-5}{(x+2)^{2}} \] = \[\int\limits \frac{-5}{u^{2}} *\frac{du}{1} = -5\int\limits \frac{1}{u^{2}} = -5* \frac{u^{-1}}{-1}= -5*\frac{(x+2)^{-1}}{-1} \]

\[= 6\ln(x+2) - 5*\frac{(x+2)^{-1}}{-1}+ C \]