Integration: 𝛿(x+2)/(x-1)dx = (x-1)+3ln(x-1)

[crack_head]

Could anyone please tell me why is the integration of ∫(x+2)/(x-1)dx ≠ (x-1)+3ln(x-1).

I got it using substitution of u=x+1.

 

[vanhees71]

I'd do the integral as follows
\int \mathrm{d} x \frac{x+2}{x-1}=\int \mathrm{d} x \frac{x-1+3}{x-1} = \int \mathrm{d} x \left (1+\frac{3}{x-1} \right )=x+3 \ln(|x-1|)+C.
So up to your missing modulus under the log (which only means that your result is valis for x>1 only), you got the correct solution. Why do you think it's wrong?

 

[crack_head]

I was confused.

Thanks