Can someone please help with this problem?

∫ (x+4)/(x^2+8x)

This is what I have so far:

∫ (x+4)/ x(x+8)

ln (x) *(∫(x+4)-∫ (x+8))

And this is where I am getting confused.

- Feb 7th 2010, 09:16 AMoperaphantom2003Integration problem....don't want answer just need missing steps
Can someone please help with this problem?

∫ (x+4)/(x^2+8x)

This is what I have so far:

∫ (x+4)/ x(x+8)

ln (x) *(∫(x+4)-∫ (x+8))

And this is where I am getting confused. - Feb 7th 2010, 09:25 AMArchie Meade
hi operaphantom2003,

instead, take $\displaystyle u=x^2+8x$

since, differentiating this gives the numerator.

$\displaystyle \frac{du}{dx}=2x+8=2(x+4)\ \Rightarrow\ \frac{du}{2}=(x+4)dx$

Now you only need solve the integral

$\displaystyle \frac{1}{2}\int{\frac{du}{u}}$ - Feb 7th 2010, 09:46 AMoperaphantom2003
Now I'm more confused. Thanks for trying.

- Feb 7th 2010, 09:49 AMArchie Meade
You should study the technique of using substitutions in integration.

That was the point of giving you that problem,

to see if you could recognise the connection between numerator and denominator.

When one is the derivative of the other, or a multiple of that derivative,

you can then write the integral in a simple form.