find the indefinite integral of (5x + 21)/(x^2 + 10x + 25) dx

Question

turingtest · Answer

are you familiar with partial fractions?

anonymous · Answer

not at all, i didn't figure i would have to use it for this question

anonymous · Answer

i evaluated it earlier using integration by parts and got $$5\ln (x + 5) - \frac{ 5x + 21 }{ x + 5 }$$
it differentiates back to the original function but it's not what i get on my TI...

turingtest · Answer

it's likely that you can manipulate the answer your TI gives you into the same, could you type it please?

anonymous · Answer

sure, my TI gives me $$5\ln(x+5) + \frac{ 4 }{ x+5 }$$

phi · Answer

they look different.  I would go with the TI on this one.

turingtest · Answer

I'd agree, you likely made a mistake

anonymous · Answer

hmm, i suppose so
can this function not be integrated without using partial fractions? maybe that's where i messed up

turingtest · Answer

I think pf is really the way to go here

phi · Answer

This is surprising, but if we ask is there a constant (of integration) that makes these 2 expression equal:

$$ - \frac{ 5x + 21 }{ x + 5 } = \frac{ 4 }{ x + 5 } + C$$
we find
$$ C=  \frac{ -5x -21 - 4 }{ x + 5 } = \frac{ -5(x+5)}{(x+5)} = -5 $$
for x≠5

so the two results are equal (to a constant)

anonymous · Answer

i was on the verge of that revelation myself just now, but in much more abstract terms--thanks for clearing that up