Integration help please.

[purpledragooon]

I actually have several questions but to start. Integrate (((x+2)/(x-1))²(dx/x)). I have tried integrating by parts but somewhere I seem to mess up. On a different note for integrating ((dx)/((x+1)(2x+1))) I got ln(2x+1)-ln(x+1) + c is this correct? Please I really need help with knowing how to do these as well what the correct answer is.

 

[pka]

I actually have several questions but to start. Integrate (((x+2)/(x-1))²(dx/x)). I have tried integrating by parts but somewhere I seem to mess up. On a different note for integrating ((dx)/((x+1)(2x+1))) I got ln(2x+1)-ln(x+1) + c is this correct? Please I really need help with knowing how to do these as well what the correct answer is.

Look at this web page. Cick the show steps tab.

 

[lookagain]

I actually have several questions but to start. Integrate (((x+2)/(x-1))²(dx/x)). I have tried integrating by parts but somewhere I seem to mess up. On a different note for integrating ((dx)/((x+1)(2x+1))) I got ln(2x+1)-ln(x+1) + c is this correct? Please I really need help with knowing how to do these as well what the correct answer is.

It would be by partial fractions:

* Edit: I read it wrong.


The integral of \(\displaystyle \dfrac{(x + 2)^2}{x(x - 1)^2} dx\)

 

[Deleted member 4993]

The partial fraction decomposition should be:

\(\displaystyle \dfrac{(x+2)^2}{x(x - 1)^2} \ = \ \dfrac{A}{x} \ + \dfrac{B}{x - 1} \ + \dfrac{C}{(x - 1)^2} \)

 

[Deleted member 4993]

... integrating ((dx)/((x+1)(2x+1))) I got ln(2x+1)-ln(x+1) + c is this correct?

Differentiate ln(2x+1) - ln(x+1) + c

If you get the original expression [1/{(x+1)(2x+1)}] back - you are most probably correct.