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Integral Calculus> integrate the following integral ∫ (2x – ...

question mark

integrate the following integral
∫ (2x – 1) / (x – 1)^2 dx

taniska , 11 Years ago

Grade 12

1 Answers

Jitender Singh

Last Activity: 11 Years ago

Ans:
Hello Student,
Please find answer to your question below

$I = \int \frac{2x-1}{(x-1)^2}dx$
$I = \int \frac{2x-2+1}{(x-1)^2}dx$
$I = \int \frac{2(x-1)+1}{(x-1)^2}dx$
$I = \int [\frac{2}{x-1}+\frac{1}{(x-1)^2}]dx$
$I = \int \frac{2}{x-1}dx+\int \frac{1}{(x-1)^2}dx$
$I = 2log(x-1)+\int \frac{1}{(x-1)^2}dx$
$I = 2log(x-1)-\frac{1}{(x-1)}+c$

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