Problem solving a parametric indefinite integral

  • Thread starter greg_rack
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  • #1
greg_rack
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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?
 

Answers and Replies

  • #2
BvU
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But doesn't correspond to the right integral.
Says who ?

##\ ##
 
  • #3
greg_rack
Gold Member
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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 :)
 

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