Hello, I have completely forgotten the procedure for integrating fractions such as the following. Can someone please show me the procedure. Thanks kindly for any help.
1/x
answer = (x^2)/4
and
sin3x / 3
The answer to your first one is wrong. $\displaystyle \displaystyle \begin{align*} \frac{d}{dx}\left(\ln{|x|}\right) = \frac{1}{x} \end{align*}$. What does that tell you about $\displaystyle \displaystyle \begin{align*} \int{\frac{1}{x}\,dx} \end{align*}$?
For $\displaystyle \displaystyle \begin{align*} \int{\frac{\sin{(3x)}}{3}\,dx} = \frac{1}{9}\int{3\sin{(3x)}\,dx} \end{align*}$, use a substitution $\displaystyle \displaystyle \begin{align*} u = 3x \implies du = 3\,dx \end{align*}$.