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

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

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
6 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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