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Problem solving a parametric indefinite integral
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[QUOTE="greg_rack, post: 6486231, member: 672853"] [B]Homework Statement:[/B] $$\int \frac{h}{ky(h-y)} \ dy$$ Where ##h##, ##k## are real numbers [B]Relevant Equations:[/B] 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? [/QUOTE]
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Problem solving a parametric indefinite integral
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