Question

integration of (6x+9)dx

Answer 1

\[
\int 6x+9~dx=6\int x~dx+9\int dx
\]

Answer 2

integrate both terms separately.
Whever we have the integral of a linear or n-graded polynomial, we integrate each term since that's the property of the integral of the addition of expressions.
\[\int\limits_{}^{} (a_1 x^n+ a _{2}x ^{n-1}+...a _{n-1}x+a_n)dx= \int\limits a_1 x^ndx + \int\limits a_2 x ^{n-1}dx+... \int\limits a _{n-1}x+ \int\limits a_n \]
looks a little complex at first sight, but for example, say i have the following integral:
\[\int\limits (x^2+5x+9 )dx\]
by the property I showed you earlier, the integral can be separated like this:
\[\int\limits x^2dx+ \int\limits 5xdx+ \int\limits 9dx\]
now, it's a matter of solving each individually:
\[\frac{ x^3 }{ 3 }+\frac{ 5x^2 }{ 2 }+9x+c\]