# Integration by parts ln(x^2+14x+24)

• cmantzioros

∫ ln(x^2+14x+24)

## Homework Equations

Integration by parts: ∫ udv = uv - ∫ vdu

## The Attempt at a Solution

I chose u = ln(x^2+14x+24) and dv = dx therefore

du = 2x+14/x^2+14x+24 and v = x

Then once I substitute, I get:

∫ ln(x^2+14x+24) = xln(x^2+14x+24) - ∫ (x(2x+14))/x^2+14x+24

Now I can't figure out how to integrate ∫ (x(2x+14))/x^2+14x+24. I've tried multiplying out, factoring. I thought I might have to use integration by parts again but it's not working out. Any help would be greatly appreciated. Thanks.

Try factoring
x^2+14x+24=(x+2)(x+12)
ln(ab)=ln(a)+ln(b)

for the method you used:

to integrate the remaining quotient, use long division and then partial fraction.

*by the way, you should put dx in your integral... some prof. take points off for that.

As they should, forgetting your differential is a crime!

And yes, christianjbs idea is quite easier

In fact, if you see ANY quadratic equation inside LN, factor it, even if the solutions are ugly. Makes things much easier.