Blessing237
Blessing237
29-06-2017
Mathematics
contestada
Integral of 1/ (a+b-(a-b)x*) dx
where (0
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LammettHash
LammettHash
30-06-2017
[tex]\displaystyle\int\frac{\mathrm dx}{a+b-(a-b)x}=\frac1{b-a}\int\frac{\mathrm dy}y[/tex]
where [tex]y=a+b-(a-b)x\implies \mathrm dy=(b-a)\,\mathrm dx[/tex]. Then
[tex]\displaystyle\frac1{b-a}\int\frac{\mathrm dy}y=\frac{\ln|y|}{b-a}+C[/tex]
[tex]\displaystyle\int\frac{\mathrm dx}{a+b-(a-b)x}=\frac{\ln|a+b-(a-b)x|}{b-a}+C[/tex]
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