Integral keeps showing wrong answer

I have been doing the integral of f=(8*x-4)/(4*x^2-4*x+5) with matlab, however, it keeps giving the wrong answer, could you help me spot whether I did something wrong with my codes? Or is it a problem of matlab?

PS: the correct answer should be log(4*x^2−4*x+5)+c, but matlab keeps showing log(x^2 - x + 5/4) (yeah I know that matlab doesn't show "+c", but still, the answer is wrong).

Answer 1

[Star Strider]

It appears to be correct, simply simplified:

syms x 
f = (8*x-4)/(4*x^2-4*x+5);
fint = int(f)
dfint = diff(fint)

figure
fplot(f, [-10 10])
hold on
fplot(dfint, [-10 10], '--')
hold off

The two plots are the same.

[Graciano Ding]

Hmmm ok thank you so much

[Star Strider]

My pleasure!

If my Answer helped you solve your problem, please Accept it!

Answer 2

[Walter Roberson]

Log of something multiplied by 4 is equal to log 4 plus log of the something. log 4 is an additive constant and indefinite integrals can have arbitrary additive constants. Therefore both versions are correct.

MATLAB considers division (your proposed 5/4) to be more expensive than multiplication so it prefers the version without the division.