Problem solving a parametric indefinite integral

[greg_rack]

Homework Statement

$$\int \frac{h}{ky(h-y)} \ dy$$
Where $h$, $k$ are real numbers

Relevant Equations

none

Since $h$ and $k$ are constants:
$$\frac{h}{k}\cdot \int \frac{1}{y(h-y)} \ dy$$
Now, rewriting the integrating function in terms of coefficients $A$ and $B$:
$$\frac{1}{y(h-y)}=\frac{A}{y}+\frac{B}{h-y}\rightarrow B=A=\frac{1}{h} \rightarrow$$
$$\frac{1}{h}\int \frac{1}{y}\ dy + \frac{1}{h}\int \frac{1}{h-y}\ dy\rightarrow \frac{ln|y|}{h}-\frac{ln|h-y|}{h}+C$$
Which, multiplied by $\frac{h}{k}$, becomes:
$$\frac{ln|\frac{y}{h-y}|}{k}+C_1$$
That doesn't correspond to the right integral.

Where did I get it wrong?

 

[BvU]

But doesn't correspond to the right integral.

Says who ?

$\$

 

[greg_rack]

Says who ?

$\$

Nevermind, my bad... my reference did just wrote $ln|\frac{y}{h-y}|$ in the, of course, equivalent form $-ln|\frac{h}{y}-1|$, and I haven't been able to see it at first sight :)