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Grade 12Integral Calculus

integrate the following integral
∫ (3x – 1) / (x – 2)^2 dx

taniska

11 Years agoGrade 12

1 Answer

Jitender Singh

11 Years ago

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

$I = \int \frac{3x-1}{(x-2)^2}dx$
$I = \int \frac{x+2x-1}{(x-2)^2}dx$
$I = \int \frac{x-2+2+2x-1}{(x-2)^2}dx$
$I = \int \frac{(x-2)+2(x-2)+5}{(x-2)^2}dx$
$I = \int [\frac{3}{x-2}+\frac{5}{(x-2)^2}]dx$
$I = \int \frac{3}{x-2}dx+\int \frac{5}{(x-2)^2}dx$
$I = 3log(x-2)- \frac{5}{(x-2)}+c$

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