1. ## simple rational integration

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

and

sin3x / 3

2. ## Re: simple rational integration

Originally Posted by fran1942
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

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*}.

3. ## Re: simple rational integration

thanks, I understand sin3x/3,. Is the integral of 1/x simply ln(x) ?

If so how would that apply to integrating 'x/3' ?

4. ## Re: simple rational integration

Originally Posted by fran1942
thanks, I understand sin3x/3, but I am still confused over how to integrate 1/x.

If you could show me the steps involved in that and also how to integrate 'x/3', then I will get it.

Do you understand the integration is the opposite of differentiation?

Also, x/3 = (1/3)x. Surely you can integrate that...

5. ## Re: simple rational integration

Originally Posted by fran1942
thanks, I understand sin3x/3,. Is the integral of 1/x simply ln(x) ?

If so how would that apply to integrating 'x/3' ?