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int(0)^(1)(dx)/((x-a)(x-b))=...

`int_(0)^(1)(dx)/((x-a)(x-b))=`

A

`(1)/(a-b)log((b-ab)/(a-ab))`

B

`log((a-ab)/(b-ab))`

C

`(1)/(2ab)log((a+ab)/(b+ab))`

D

`(1)/(ab)tan^(-1)((a-ab)/(b-ab))`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the integral \[ I = \int_{0}^{1} \frac{dx}{(x-a)(x-b)} \] we will follow these steps: ### Step 1: Rewrite the integrand We start by rewriting the integrand in a more manageable form. We can express the function as: \[ \frac{1}{(x-a)(x-b)} = \frac{A}{x-a} + \frac{B}{x-b} \] where \(A\) and \(B\) are constants that we will determine.
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