Question

Integration by partial fractions...

integrate (5x+2) / (2x^2 + x)

Pleaseeee show your steps, I keep getting:

2ln(x) + ln(2x + 1) + C. But I believe this is not the correct answer.

Answer 1

wolfram says answer is

2ln(x) + (1/2)ln(2x + 1) + C

i didn't try to solve it but do you see where the mistake is?

Answer 2

It's REALLY close. Wolfram does not quite have it right.

Should be: \(2ln(|x|) + (1/2)ln(|2x+1|) + C\)

We don't know anything about x in the indefinite integral. The absolute values are NOT optional.

Why is it integration by parts? Try partial fractions.

Answer 3

My mistake I meant to say partial fractions... :P

Answer 4

I don't see why there is a 1/2 on the second expression

Answer 5

\(\int \dfrac{1}{x+1}\;dx = ln(|x+1| + C)\)

\(\int \dfrac{1}{2x+1}\;dx = (1/2)ln(|2x+1| + C)\)

\(\int \dfrac{1}{\pi x+1}\;dx = (1/\pi)ln(|\pi x+1| + C)\)

Think "Chain Rule".

Answer 6

Wow I understand now... I skipped the substitution step and just put the expression in ln(_)

Answer 7

but with substitution there will be a fraction, correct? in this case u = 2x + 1, du = 2 dx, dx = 1/2 du which is where the 1/2 comes from

Answer 8

yes! thank you!

Answer 9

Well, there you have it. Good work.